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Frozen Jacobian multistep iterative method for solving nonlinear IVPs and BVPs

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Ahmad, Fayyaz
Shafiq Ur, Rehman
Ullah, Malik Zaka
Aljahdali, Hani Moaiteq
Alshomrani, Ali Saleh
Carrasco, Juan A.Més informacióMés informacióMés informació
Ahmad, Shamshad
Document typeArticle
Defense date2017-01-01
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
Abstract
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.
CitationAhmad, F., Shafiq Ur, R., Ullah, M., Aljahdali, H., Alshomrani, A., Carrasco, J., Ahmad , S. Frozen Jacobian multistep iterative method for solving nonlinear IVPs and BVPs. "Complexity", 1 Gener 2017, vol. 2017. 
URIhttp://hdl.handle.net/2117/107350
DOI10.1155/2017/9407656
ISSN1076-2787
Publisher versionhttps://www.hindawi.com/journals/complexity/2017/9407656/
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