Resolución numérica de problemas diferenciales por el Método de Soluciones Fundamentales

Abstract

This work examines the Method of Fundamental Solutions (MFS) together with other meshless numerical methods, such as the Method of Particular Solutions, for solving differential problems, both direct and inverse. The theoretical construction of the method is formalized in the context of partial differential equations (PDEs) using fundamental notions from Distribution Theory. The main objective has been to develop a practical approach, illustrated through classical examples that demonstrate the applicability and efficiency of the MFS to various types of problems (elliptic, parabolic and hyperbolic), as well as to provide MATLAB codes for effective resolution. A general description of the MFS is presented, supported by a collection of applied examples and their corresponding computational implementations, which can serve both as an introduction to meshless methods as a starting point for their extension to more complex problems.