Numerical Solution of Fourth Order Homogeneous Parabolic Partial Differential Equations (PDEs) using Non-Polynomial Cubic Spline Method (NPCSM)

Abstract

Non-polynomial cubic spline functions are already being used in the field of engineering, computer sciences, and natural sciences to solve ordinary differential equations (ODEs) and partial differential equations (PDEs). However, many of the above-mentioned problems do not have an exact, stable, or convergent exact solution. There are different approximations and methods that can be applied to solve these problems. This study implemented the purposed method on homogeneous parabolic PDEs having different dimensions. The results obtained were compared with the exact solution and results of other existing methods in tabular and graphical form. Mathematica was used to find the mathematical and graphical results.EMATICA. Keywords: Adomian decomposition method (ADM), non-polynomial cubic spline method (NPCSM), continuous approximation, finite difference approximations, fourth order homogeneous parabolic partial differential equations (PDEs) Copyright(c) The Authors