Numerical solution of second-order nonlinear partial differential equations originating from physical phenomena using Hermite based block methods

Abstract

A Hermite based block method (HBBM) is proposed for the numerical solution of second-order non-linear elliptic partial differential equations (PDEs). The development of the method was accomplished through the methodology of interpolation and collocation procedures. The method’s analysis reveals that it satisfied the requirements for a numerical technique to be convergent. The implementation of the method is extensively discussed. Five numerical examples originating from physical phenomena are presented, and the applicability and accuracy of the HBBM are established by comparing them with the existing methods; the haar wavelet collocation method, the modified cubic B-spline collocation method, and the modified decomposition method. The proposed methods of HBBM are more accurate, stable, and convergent

Keywords

• Hermite based block methods
• Convergence of the methods
• Hermite approximation function
• Second-order nonlinear PDEs
• Klein–Gordon equations
• Sine–Gordon equations