Reviewing the Application of Basis Function Methods in Numerical Solutions for Nonlinear Partial Differential Equations

Abstract

Numerical solutions for nonlinear partial differential equations (PDEs) play a crucial role in a wide range of scientific and engineering fields. The complexity of nonlinear PDEs often prohibits the use of analytical techniques, necessitating the development of robust and efficient numerical methods. Among these, basis function methods have garnered considerable attention due to their versatility and effectiveness in handling nonlinear problems. This review aims to provide a comprehensive overview of the application of basis function methods in solving nonlinear PDEs. The review begins by introducing the fundamental concepts of nonlinear PDEs and their significance in modeling real-world phenomena.