Solution of Parabolic Partial Differential Equations by Non-Polynomial Cubic Spline Technique

Bilal Ahmad,Fazal Dayan,Maqbool Ahmad ,Anjum Perviz

doi:10.32350/sir.53.05

Abstract

Parabolic partial differential equation having a great impact on our scientific, engineering and technology. Enormous research have been conducted for the solution of parabolic PDEs. . In this research work, we introduced a novel technique for the numerical solution of fourth order PDEs. The novel technique is based upon the polynomial cubic cutting method (PCSM) was used with Adomian breakdown technique (ADM).The constraint for the alternative variables was decomposed by Edomian decomposition for the successive approximation. A numerical test problem of parabolic PDEs solved by purposed technique

Highlights

Field of differential equations first appeared from the study of calculus by the German mathematician Leibniz (1646-1716) and Newton (1642-1727)
He did some work in differential equations, but the progress of calculus and mechanics offered a foundation for differential equations and their applications in eighteenth century
The major objective of this research article is to find out the numerical solution of fourth order parabolic partial differential equation

Summary

Introduction

Field of differential equations first appeared from the study of calculus by the German mathematician Leibniz (1646-1716) and Newton (1642-1727). [2] Omotayo, A.T.&O.M. Ogunian a nonpolynomial cubic spline method to solve the linear fourth order parabolic problem. Papamichael and Worsley [10] solution of boundary value problems with help of cubic spline method of order four.

Results

Conclusion