GAA - Grup d'Astronomia i Astrofísica
http://hdl.handle.net/2117/1136
Tue, 21 Nov 2017 14:13:42 GMT2017-11-21T14:13:42ZFirst measurement of the 34S(p,gamma)35Cl reaction rate through indirect methods for presolar nova grains
http://hdl.handle.net/2117/109218
First measurement of the 34S(p,gamma)35Cl reaction rate through indirect methods for presolar nova grains
Gillespie, S; Parikh, A.; Barton, C; Faestermann, Thomas; José Pont, Jordi; Hertenberger, R.; Wirth, Hans Friedrich; de Séréville, N; Riley, J; Williams, M
Sulphur isotopic ratio measurements may help to establish the astrophysical sites in which certain presolar grains were formed. Nova model predictions of the 34S/32S ratio are, however, unreliable due to the lack of an experimental 34S(p,¿)35Cl reaction rate. To this end, we have measured the 34S(3He,d)35Cl reaction at 20 MeV using a high resolution quadrupole-dipole-dipole-dipole magnetic spectrograph. Twenty-two levels over 6.2 MeV <Ex(35Cl)<7.4 MeV were identified, ten of which were previously unobserved. Proton-transfer spectroscopic factors have been measured for the first time over the energy range relevant for novae. With this new spectroscopic information a new 34S(p,¿)35Cl reaction rate has been determined using a Monte Carlo method. Hydrodynamic nova model calculations have been performed using this new reaction rate. These models show that remaining uncertainties in the 34S(p,¿) rate affect nucleosynthesis predictions by less than a factor of 1.4, and predict a 34S/32S isotopic ratio of 0.014–0.017. Since recent type II supernova models predict 34S/32S=0.026-0.053, the 34S/32S isotopic ratio may be used, in conjunction with other isotopic signatures, to distinguish presolar grains from oxygen-neon nova and type II supernova origin. Our results address a key nuclear physics uncertainty on which recent considerations discounting the nova origin of several grains depend.
Wed, 25 Oct 2017 16:39:16 GMThttp://hdl.handle.net/2117/1092182017-10-25T16:39:16ZGillespie, SParikh, A.Barton, CFaestermann, ThomasJosé Pont, JordiHertenberger, R.Wirth, Hans Friedrichde Séréville, NRiley, JWilliams, MSulphur isotopic ratio measurements may help to establish the astrophysical sites in which certain presolar grains were formed. Nova model predictions of the 34S/32S ratio are, however, unreliable due to the lack of an experimental 34S(p,¿)35Cl reaction rate. To this end, we have measured the 34S(3He,d)35Cl reaction at 20 MeV using a high resolution quadrupole-dipole-dipole-dipole magnetic spectrograph. Twenty-two levels over 6.2 MeV <Ex(35Cl)<7.4 MeV were identified, ten of which were previously unobserved. Proton-transfer spectroscopic factors have been measured for the first time over the energy range relevant for novae. With this new spectroscopic information a new 34S(p,¿)35Cl reaction rate has been determined using a Monte Carlo method. Hydrodynamic nova model calculations have been performed using this new reaction rate. These models show that remaining uncertainties in the 34S(p,¿) rate affect nucleosynthesis predictions by less than a factor of 1.4, and predict a 34S/32S isotopic ratio of 0.014–0.017. Since recent type II supernova models predict 34S/32S=0.026-0.053, the 34S/32S isotopic ratio may be used, in conjunction with other isotopic signatures, to distinguish presolar grains from oxygen-neon nova and type II supernova origin. Our results address a key nuclear physics uncertainty on which recent considerations discounting the nova origin of several grains depend.A Trojan horse approach to the production of 18F in Novae
http://hdl.handle.net/2117/109215
A Trojan horse approach to the production of 18F in Novae
la Cognata, M; Pizzone, R; José Pont, Jordi; Hernanz Carbó, Margarita; Cherubini, S; Gulino, M; Rapisarda, G; Spitaleri, C
Crucial information on nova nucleosynthesis can be potentially inferred from ¿-ray signals powered by 18F decay. Therefore, the reaction network producing and destroying this radioactive isotope has been extensively studied in the last years. Among those reactions, the 18F(p, a)15O cross-section has been measured by means of several dedicated experiments, both using direct and indirect methods. The presence of interfering resonances in the energy region of astrophysical interest has been reported by many authors including the recent applications of the Trojan Horse Method. In this work, we evaluate what changes are introduced by the Trojan Horse data in the 18F(p, a)15O astrophysical factor recommended in a recent R-matrix analysis, accounting for existing direct and indirect measurements. Then the updated reaction rate is calculated and parameterized and implications of the new results on nova nucleosynthesis are thoroughly discussed.
Wed, 25 Oct 2017 16:23:24 GMThttp://hdl.handle.net/2117/1092152017-10-25T16:23:24Zla Cognata, MPizzone, RJosé Pont, JordiHernanz Carbó, MargaritaCherubini, SGulino, MRapisarda, GSpitaleri, CCrucial information on nova nucleosynthesis can be potentially inferred from ¿-ray signals powered by 18F decay. Therefore, the reaction network producing and destroying this radioactive isotope has been extensively studied in the last years. Among those reactions, the 18F(p, a)15O cross-section has been measured by means of several dedicated experiments, both using direct and indirect methods. The presence of interfering resonances in the energy region of astrophysical interest has been reported by many authors including the recent applications of the Trojan Horse Method. In this work, we evaluate what changes are introduced by the Trojan Horse data in the 18F(p, a)15O astrophysical factor recommended in a recent R-matrix analysis, accounting for existing direct and indirect measurements. Then the updated reaction rate is calculated and parameterized and implications of the new results on nova nucleosynthesis are thoroughly discussed.An efficient method for the static deflection analysis of an infinite beam on a nonlinear elastic foundation of one-way spring model
http://hdl.handle.net/2117/108739
An efficient method for the static deflection analysis of an infinite beam on a nonlinear elastic foundation of one-way spring model
Ahmad, Fayyaz; Ullah, Malik Zaka; Jang, Taek Soo; Alaidarous, Eman
An efficient numerical iterative method is constructed for the static deflection of an infinite beam on a nonlinear elastic foundation. The proposed iterative scheme consists of quasilinear method (QLM) and Green’s function technique. The QLM translates the nonlinear ordinary differential equation into iterative linear ordinary differential equation. The successive iterations of quasilinear form of ordinary differential equation (ODE) show the quadratic convergence if an initial guess is chosen in the neighbourhood of true solution. The Green’s function technique converts the differential operator into an integral operator and the integral operator is approximated by discrete summation which finally gives us an iterative formula for the resulting set of algebraic equations.The numerical validity and efficiency are proved by simulating some nonlinear problems.
Tue, 17 Oct 2017 08:29:35 GMThttp://hdl.handle.net/2117/1087392017-10-17T08:29:35ZAhmad, FayyazUllah, Malik ZakaJang, Taek SooAlaidarous, EmanAn efficient numerical iterative method is constructed for the static deflection of an infinite beam on a nonlinear elastic foundation. The proposed iterative scheme consists of quasilinear method (QLM) and Green’s function technique. The QLM translates the nonlinear ordinary differential equation into iterative linear ordinary differential equation. The successive iterations of quasilinear form of ordinary differential equation (ODE) show the quadratic convergence if an initial guess is chosen in the neighbourhood of true solution. The Green’s function technique converts the differential operator into an integral operator and the integral operator is approximated by discrete summation which finally gives us an iterative formula for the resulting set of algebraic equations.The numerical validity and efficiency are proved by simulating some nonlinear problems.Updated evolutionary sequences for hydrogen-deficient white dwarfs
http://hdl.handle.net/2117/108520
Updated evolutionary sequences for hydrogen-deficient white dwarfs
Camisassa, Maria E; Althaus, Leandro G.; Rohrmann, René D.; García-Berro Montilla, Enrique; Torres Gil, Santiago; Corsico, Alejandro H.; Wachlin, Felipe C.
We present a set of full evolutionary sequences for white dwarfs with hydrogen-deficient atmospheres. We take into account the evolutionary history of the progenitor stars, all the relevant energy sources involved in the cooling, element diffusion in the very outer layers, and outer boundary conditions provided by new and detailed non-gray white dwarf model atmospheres for pure helium composition. These model atmospheres are based on the most up-to-date physical inputs. Our calculations extend down to very low effective temperatures, of ~2500 K, provide a homogeneous set of evolutionary cooling tracks that are appropriate for mass and age determinations of old hydrogen-deficient white dwarfs, and represent a clear improvement over previous efforts, which were computed using gray atmospheres.
Mon, 09 Oct 2017 12:12:17 GMThttp://hdl.handle.net/2117/1085202017-10-09T12:12:17ZCamisassa, Maria EAlthaus, Leandro G.Rohrmann, René D.García-Berro Montilla, EnriqueTorres Gil, SantiagoCorsico, Alejandro H.Wachlin, Felipe C.We present a set of full evolutionary sequences for white dwarfs with hydrogen-deficient atmospheres. We take into account the evolutionary history of the progenitor stars, all the relevant energy sources involved in the cooling, element diffusion in the very outer layers, and outer boundary conditions provided by new and detailed non-gray white dwarf model atmospheres for pure helium composition. These model atmospheres are based on the most up-to-date physical inputs. Our calculations extend down to very low effective temperatures, of ~2500 K, provide a homogeneous set of evolutionary cooling tracks that are appropriate for mass and age determinations of old hydrogen-deficient white dwarfs, and represent a clear improvement over previous efforts, which were computed using gray atmospheres.The population of white dwarf-main sequence binaries in the SDSS DR 12
http://hdl.handle.net/2117/107977
The population of white dwarf-main sequence binaries in the SDSS DR 12
Cojocaru, Elena Ruxandra; Rebassa Mansergas, Alberto; Torres Gil, Santiago; García-Berro Montilla, Enrique
We present a Monte Carlo population synthesis study of white dwarf-main sequence (WD+MS) binaries in the Galactic disc aimed at reproducing the ensemble properties of the entire population observed by the Sloan Digital Sky Survey (SDSS) Data Release 12. Our simulations take into account all known observational biases and use the most up-to-date stellar evolutionary models. This allows us to perform a sound comparison between the simulations and the observational data. We find that the properties of the simulated and observed parameter distributions agree best when assuming low values of the common envelope efficiency (0.2-0.3), a result that is in agreement with previous findings obtained by observational and population synthesis studies of close SDSSWD+MS binaries.We also show that all synthetic populations that result from adopting an initial mass ratio distribution with a positive slope are excluded by observations. Finally, we confirm that the properties of the simulated WD+MS binary populations are nearly independent of the age adopted for the thin disc, on the contribution of WD+MS binaries from the thick disc (0-17 per cent of the total population) and on the assumed fraction of the internal energy that is used to eject the envelope during the common envelope phase (0.1-0.5).
Mon, 25 Sep 2017 16:18:30 GMThttp://hdl.handle.net/2117/1079772017-09-25T16:18:30ZCojocaru, Elena RuxandraRebassa Mansergas, AlbertoTorres Gil, SantiagoGarcía-Berro Montilla, EnriqueWe present a Monte Carlo population synthesis study of white dwarf-main sequence (WD+MS) binaries in the Galactic disc aimed at reproducing the ensemble properties of the entire population observed by the Sloan Digital Sky Survey (SDSS) Data Release 12. Our simulations take into account all known observational biases and use the most up-to-date stellar evolutionary models. This allows us to perform a sound comparison between the simulations and the observational data. We find that the properties of the simulated and observed parameter distributions agree best when assuming low values of the common envelope efficiency (0.2-0.3), a result that is in agreement with previous findings obtained by observational and population synthesis studies of close SDSSWD+MS binaries.We also show that all synthetic populations that result from adopting an initial mass ratio distribution with a positive slope are excluded by observations. Finally, we confirm that the properties of the simulated WD+MS binary populations are nearly independent of the age adopted for the thin disc, on the contribution of WD+MS binaries from the thick disc (0-17 per cent of the total population) and on the assumed fraction of the internal energy that is used to eject the envelope during the common envelope phase (0.1-0.5).Frozen Jacobian multistep iterative method for solving nonlinear IVPs and BVPs
http://hdl.handle.net/2117/107350
Frozen Jacobian multistep iterative method for solving nonlinear IVPs and BVPs
Ahmad, Fayyaz; Shafiq Ur, Rehman; Ullah, Malik Zaka; Aljahdali, Hani Moaiteq; Alshomrani, Ali Saleh; Carrasco, Juan A.; Ahmad, Shamshad
In this paper, we present and illustrate a frozen Jacobian multistep iterative method to solve systems of nonlinear equations associated with initial value problems (IVPs) and boundary value problems (BVPs). We have used Jacobi-Gauss-Lobatto collocation (J-GL-C) methods to discretize the IVPs and BVPs. Frozen Jacobian multistep iterative methods are computationally very efficient. They require only one inversion of the Jacobian in the form of LU-factorization. The LU factors can then be used repeatedly in the multistep part to solve other linear systems. The convergence order of the proposed iterative method is , where is the number of steps. The validity, accuracy, and efficiency of our proposed frozen Jacobian multistep iterative method is illustrated by solving fifteen IVPs and BVPs. It has been observed that, in all the test problems, with one exception in this paper, a single application of the proposed method is enough to obtain highly accurate numerical solutions. In addition, we present a comprehensive comparison of J-GL-C methods on a collection of test problems.
Mon, 04 Sep 2017 10:11:11 GMThttp://hdl.handle.net/2117/1073502017-09-04T10:11:11ZAhmad, FayyazShafiq Ur, RehmanUllah, Malik ZakaAljahdali, Hani MoaiteqAlshomrani, Ali SalehCarrasco, Juan A.Ahmad, ShamshadIn this paper, we present and illustrate a frozen Jacobian multistep iterative method to solve systems of nonlinear equations associated with initial value problems (IVPs) and boundary value problems (BVPs). We have used Jacobi-Gauss-Lobatto collocation (J-GL-C) methods to discretize the IVPs and BVPs. Frozen Jacobian multistep iterative methods are computationally very efficient. They require only one inversion of the Jacobian in the form of LU-factorization. The LU factors can then be used repeatedly in the multistep part to solve other linear systems. The convergence order of the proposed iterative method is , where is the number of steps. The validity, accuracy, and efficiency of our proposed frozen Jacobian multistep iterative method is illustrated by solving fifteen IVPs and BVPs. It has been observed that, in all the test problems, with one exception in this paper, a single application of the proposed method is enough to obtain highly accurate numerical solutions. In addition, we present a comprehensive comparison of J-GL-C methods on a collection of test problems.The supersoft X-ray source in V5116 Sagittarii: I. the high resolution spectra
http://hdl.handle.net/2117/105104
The supersoft X-ray source in V5116 Sagittarii: I. the high resolution spectra
Sala Cladellas, Glòria; Ness, Jan-Uwe; Hernanz Carbó, Margarita; Greiner, Jochen
Context. Classical nova explosions occur on the surface of an accreting white dwarf in a binary system. After ejection of a fraction of the envelope and when the expanding shell becomes optically thin to X-rays, a bright source of supersoft X-rays arises, powered by residual H burning on the surface of the white dwarf. While the general picture of the nova event is well established, the details and balance of accretion and ejection processes in classical novae are still full of unknowns. The long-term balance of accreted matter is of special interest for massive accreting white dwarfs, which may be promising supernova Ia progenitor candidates. Nova V5116 Sgr 2005b was observed as a bright and variable supersoft X-ray source by XMM-Newton in March 2007, 610 days after outburst. The light curve showed a periodicity consistent with the orbital period. During one third of the orbit the luminosity was a factor of seven brighter than during the other two thirds of the orbital period.
Aims. In the present work we aim to disentangle the X-ray spectral components of V5116 Sgr and their variability.
Methods. We present the high resolution spectra obtained with XMM-Newton RGS and Chandra LETGS/HRC-S in March and August 2007.
Results. The grating spectrum during the periods of high-flux shows a typical hot white dwarf atmosphere dominated by absorption lines of N VI and N VII. During the low-flux periods, the spectrum is dominated by an atmosphere with the same temperature as during the high-flux period, but with several emission features superimposed. Some of the emission lines are well modeled with an optically thin plasma in collisional equilibrium, rich in C and N, which also explains some excess in the spectra of the high-flux period. No velocity shifts are observed in the absorption lines, with an upper limit set by the spectral resolution of 500 km s-1, consistent with the expectation of a non-expanding atmosphere so late in the evolution of the post-nova.
Fri, 02 Jun 2017 06:35:06 GMThttp://hdl.handle.net/2117/1051042017-06-02T06:35:06ZSala Cladellas, GlòriaNess, Jan-UweHernanz Carbó, MargaritaGreiner, JochenContext. Classical nova explosions occur on the surface of an accreting white dwarf in a binary system. After ejection of a fraction of the envelope and when the expanding shell becomes optically thin to X-rays, a bright source of supersoft X-rays arises, powered by residual H burning on the surface of the white dwarf. While the general picture of the nova event is well established, the details and balance of accretion and ejection processes in classical novae are still full of unknowns. The long-term balance of accreted matter is of special interest for massive accreting white dwarfs, which may be promising supernova Ia progenitor candidates. Nova V5116 Sgr 2005b was observed as a bright and variable supersoft X-ray source by XMM-Newton in March 2007, 610 days after outburst. The light curve showed a periodicity consistent with the orbital period. During one third of the orbit the luminosity was a factor of seven brighter than during the other two thirds of the orbital period.
Aims. In the present work we aim to disentangle the X-ray spectral components of V5116 Sgr and their variability.
Methods. We present the high resolution spectra obtained with XMM-Newton RGS and Chandra LETGS/HRC-S in March and August 2007.
Results. The grating spectrum during the periods of high-flux shows a typical hot white dwarf atmosphere dominated by absorption lines of N VI and N VII. During the low-flux periods, the spectrum is dominated by an atmosphere with the same temperature as during the high-flux period, but with several emission features superimposed. Some of the emission lines are well modeled with an optically thin plasma in collisional equilibrium, rich in C and N, which also explains some excess in the spectra of the high-flux period. No velocity shifts are observed in the absorption lines, with an upper limit set by the spectral resolution of 500 km s-1, consistent with the expectation of a non-expanding atmosphere so late in the evolution of the post-nova.Measurement of key resonance states for the 40P(p,g)31S reaction rate, and the production of intermediate-mass elements in nova explosions
http://hdl.handle.net/2117/104927
Measurement of key resonance states for the 40P(p,g)31S reaction rate, and the production of intermediate-mass elements in nova explosions
Kankainen, A; Woods, P.J.; Schatz, H.; Poxon-Pearson, T; Doherty, D.T.; Bader, V.; Baugher, T.; Bazin, D.; Brown, B.A.; Browne, J.; Estrade, A.; Gade, A.; José Pont, Jordi; Kontos, A.; Langer, C.; Lotay, G.; Meisel, Z.; Montes, F.; Noji, S.; Nunes, F.; Perdikakis, G.; Pereira, J.; Recchia, F.; Redpath, T.; Stroberg, R.; Scott, M.; Seweryniak, D.; Stevens, J.; Weisshaar, D.; Wimmer, K.; Zegers, R.
We report the first experimental constraints on spectroscopic factors and strengths of key resonances in the 30P(p, γ)31Sreaction critical for determining the production of intermediate-mass elements up to Ca in nova ejecta. The 30P(d, n)31Sreaction was studied in inverse kinematics using the GRETINA γ-ray array to measure the angle-integrated cross-sections of states above the proton threshold. In general, negative-parity states are found to be most strongly produced but the absolute values of spectroscopic factors are typically an order of magnitude lower than predicted by the shell-model calculations employing WBP Hamiltonian for the negative-parity states. The results clearly indicate the dominance of a single 3/2−resonance state at 196 keV in the region of nova burning T≈0.10–0.17GK, well within the region of interest for nova nucleosynthesis. Hydrodynamic simulations of nova explosions have been performed to demonstrate the effect on the composition of nova ejecta.
Fri, 26 May 2017 12:44:57 GMThttp://hdl.handle.net/2117/1049272017-05-26T12:44:57ZKankainen, AWoods, P.J.Schatz, H.Poxon-Pearson, TDoherty, D.T.Bader, V.Baugher, T.Bazin, D.Brown, B.A.Browne, J.Estrade, A.Gade, A.José Pont, JordiKontos, A.Langer, C.Lotay, G.Meisel, Z.Montes, F.Noji, S.Nunes, F.Perdikakis, G.Pereira, J.Recchia, F.Redpath, T.Stroberg, R.Scott, M.Seweryniak, D.Stevens, J.Weisshaar, D.Wimmer, K.Zegers, R.We report the first experimental constraints on spectroscopic factors and strengths of key resonances in the 30P(p, γ)31Sreaction critical for determining the production of intermediate-mass elements up to Ca in nova ejecta. The 30P(d, n)31Sreaction was studied in inverse kinematics using the GRETINA γ-ray array to measure the angle-integrated cross-sections of states above the proton threshold. In general, negative-parity states are found to be most strongly produced but the absolute values of spectroscopic factors are typically an order of magnitude lower than predicted by the shell-model calculations employing WBP Hamiltonian for the negative-parity states. The results clearly indicate the dominance of a single 3/2−resonance state at 196 keV in the region of nova burning T≈0.10–0.17GK, well within the region of interest for nova nucleosynthesis. Hydrodynamic simulations of nova explosions have been performed to demonstrate the effect on the composition of nova ejecta.A Parameterized multi-step Newton method for solving systems of nonlinear equations
http://hdl.handle.net/2117/104811
A Parameterized multi-step Newton method for solving systems of nonlinear equations
Ahmad, Fayyaz; Tohidi, Emran; Carrasco, Juan A.
We construct a novel multi-step iterative method for solving systems of nonlinear equations by introducing a parameter. to generalize the multi-step Newton method while keeping its order of convergence and computational cost. By an appropriate selection of theta, the new method can both have faster convergence and have larger radius of convergence. The new iterative method only requires one Jacobian inversion per iteration, and therefore, can be efficiently implemented using Krylov subspace methods. The new method can be used to solve nonlinear systems of partial differential equations, such as complex generalized Zakharov systems of partial differential equations, by transforming them into systems of nonlinear equations by discretizing approaches in both spatial and temporal independent variables such as, for instance, the Chebyshev pseudo-spectral discretizing method. Quite extensive tests show that the new method can have significantly faster convergence and significantly larger radius of convergence than the multi-step Newton method.
Wed, 24 May 2017 10:09:04 GMThttp://hdl.handle.net/2117/1048112017-05-24T10:09:04ZAhmad, FayyazTohidi, EmranCarrasco, Juan A.We construct a novel multi-step iterative method for solving systems of nonlinear equations by introducing a parameter. to generalize the multi-step Newton method while keeping its order of convergence and computational cost. By an appropriate selection of theta, the new method can both have faster convergence and have larger radius of convergence. The new iterative method only requires one Jacobian inversion per iteration, and therefore, can be efficiently implemented using Krylov subspace methods. The new method can be used to solve nonlinear systems of partial differential equations, such as complex generalized Zakharov systems of partial differential equations, by transforming them into systems of nonlinear equations by discretizing approaches in both spatial and temporal independent variables such as, for instance, the Chebyshev pseudo-spectral discretizing method. Quite extensive tests show that the new method can have significantly faster convergence and significantly larger radius of convergence than the multi-step Newton method.Multi-step frozen Jacobian iterative scheme for solving IVPs and BVPs based on higher order Fréchet derivatives
http://hdl.handle.net/2117/104772
Multi-step frozen Jacobian iterative scheme for solving IVPs and BVPs based on higher order Fréchet derivatives
Ilyas, Iqra; Ali, Zulqar; Ahmad, Fayyaz; Ullah, Malik Zaka; Alshomrani, Ali Saleh
A multi-step frozen Jacobian iterative scheme for solving system of nonlinear equations associated with IVPs (initial value problems) and BVPs (boundary value problems) is constructed. The multi-step iterative schemes consist of two parts, namely base method and a multi-step part. The proposed iterative scheme uses higher order Fr ´echet derivatives in the base method part and offers high convergence order (CO) 3s + 1, here s is the number of steps.
The increment in the CO per step is three, and we solve three upper and lower triangles systems per step in the multi-step part. A single inversion of the is not working in latexfrozen Jacobian is required and in fact, we avoid the direct inversion of the frozen Jacobian by computing the LU factors. The LU-factors are utilized in the multi-step part to solve upper and lower triangular systems repeatedly that makes the iterative scheme computationally efficient. We solve a set of IVPs and BVPs to show the validity, accuracy and efficiency of our proposed iterative scheme.
Tue, 23 May 2017 11:55:56 GMThttp://hdl.handle.net/2117/1047722017-05-23T11:55:56ZIlyas, IqraAli, ZulqarAhmad, FayyazUllah, Malik ZakaAlshomrani, Ali SalehA multi-step frozen Jacobian iterative scheme for solving system of nonlinear equations associated with IVPs (initial value problems) and BVPs (boundary value problems) is constructed. The multi-step iterative schemes consist of two parts, namely base method and a multi-step part. The proposed iterative scheme uses higher order Fr ´echet derivatives in the base method part and offers high convergence order (CO) 3s + 1, here s is the number of steps.
The increment in the CO per step is three, and we solve three upper and lower triangles systems per step in the multi-step part. A single inversion of the is not working in latexfrozen Jacobian is required and in fact, we avoid the direct inversion of the frozen Jacobian by computing the LU factors. The LU-factors are utilized in the multi-step part to solve upper and lower triangular systems repeatedly that makes the iterative scheme computationally efficient. We solve a set of IVPs and BVPs to show the validity, accuracy and efficiency of our proposed iterative scheme.