A Reproducing Kernel Method for Solving a Class of Nonlinear Systems of PDEs

Abstract

This paper is concerned with a technique for solving a class of nonlinear systems of partial differential equations (PDEs) in the reproducing kernel Hilbert space. The analytical solution is represented in the form of series. An iterative method is given to obtain the approximate solution. The convergence analysis is established theoretically. The proposed method is successfully used for solving a coupled system of viscous Burgers’ equations and a nonlinear hyperbolic system. Performance of the method is tested in terms of various error norms. In the case of non-availability of exact solution, it is compared with the existing methods.

Keywords:

• reproducing kernel space
• coupled viscous Burgers’ equations
• nonlinear hyperbolic system

AMS Subject Classification:

• 65M99
• 35C10