Solving 2D time-dependent partial differential equations using the EBF meshless method

Most engineering problems lead to partial differential equations (PDEs), so solving them is one of the biggest challenges for the scientists and engineers. Obtaining the exact solution for such equations is not possible except in special cases, which implies the importance of the numerical methods. One of the methods that has been recently developed to solve PDEs, is the exponential basis functions (EBF) meshless method. Here we consider 2D time-dependent equations like heat and wave equations. In this method, the unknown function is considered as a linear combination of basis exponential functions and the unknown coefficients are obtained by using the boundary conditions. The results show excellent performance of this method for time-dependent problems.

کلیدواژه ها:

partial differential equations ، meshless methods ، heat equation ، wave equation ، exponential basis functions