Numerical Treatment of Some Types of Nonlinear Partial Differential Equations

Abstract

Over the last decade, many quality research papers and monographs have been published focusing on numerical approximations of nonlinear partial differential equations (NPDEs). These equations are very important in mathematics and relevant to the study of various real-life phenomena from nature, physics, engineering and sciences. In this thesis, the cubic B-spline (CBS), non-polynomial spline, fractional calculus and Adomian decomposing methods are used to approximate solutions to the dissipative wave, the dispersive partial differential, coupled nonlinear nonhomogeneous Klein–Gordon, linear space-fractional telegraph partial differential and generalised Burgers–Huxley equations. These approximate solutions have been proven to be stable and convergent in various studies. The numerical examples considered in this paper illustrate the efficiency of the method compared with those used in recent works published in this field.