The heat equation is known as one of the easiest PDEs to solve. However, when we consider the case where two different phases coexist, (i.e. the so-called Stefan problem), suddenly everything becomes much harder to solve, ...

Partial Differential Equations (PDEs) are widely used to simulate many scenarios in science and engineering, usually solved through iterative techniques (e.g., Jacobi, Gauss–Seidel). These methods produce an approximate ...

Saiph is a domain specific language for solving partial differential equations in high performance computing systems, developed at the Barcelona Computing Center. The aim of this project is to extend this language to support ...

The main aim of this bachelor's thesis is to introduce the concept of a ground state and prove its existence for the nonlinear diffusion equation $$ -\Delta u + a u = b |u|^\alpha u \ \ \text{in} \ \mathbb{R}^N, $$ as well ...

The research presented in this study investigates the performance of two different approaches, namely the staggered approach and the coupled approach, in simulating growth glioblastoma cells in microfluidic devices. The ...