Numerical Solution with Non-Polynomial Cubic Spline Technique of Order Four Homogeneous Parabolic Partial Differential Equations

Bilal Ahmad,Anjum Perviz,Fazal Dayan,Muhammad Ozair Ahmad

doi:10.32350/sir.54.03

Abstract

An innovative technique of NPCS are being used in engineering, computer sciences and natural sciences field to solve PDEs and ODEs Problems. There are many problems not having exact solution or not much stable and convergent exact solution, to solve such problem one apply different approximation, iterative and many other methods. The developed technique is one of them and implemented on some homogeneous parabolic PDEs of different dimensions and getting results will compare with exact solution and one other existing method, by tabular and graphically as well. Graphs and Mathematical result are found by using MATHEMATICA. Copyright(c) The Authors

Highlights

Splines are a method to model a curve using a group of points that can be mapped via mathematical technique
The major objective of this research article is the numerical solution of fourth order homogenous parabolic partial differential equation
Numerous techniques are available in literature to solve the ordinary differential equations and partial differential equations

Summary

Introduction

Splines are a method to model a curve using a group of points that can be mapped via mathematical technique. Splines and its applications have been effectively used in data fitting, optimal control problems, function approximation, integro-differential equation, Computer-Aided Geometric Design (CAGD), wavelets etc. Using the mathematical representation of the surface of an airplane instead of physical model saved thousands of measurements in the design and construction process. This method would have some obstacles in data exchange and required a mathematical method to illustrate the shape of the curve [14]. Solution of Parabolic Partial Differential Equations by NonPolynomial Cubic Spline Technique Omotayo, A.T. Ogunian a non-polynomial cubic spline method to solve the linear fourth order parabolic problem. Polynomial cubic spline method for solving fourth-order parabolic two point boundary value problems and many more. The major objective of this research article is the numerical solution of fourth order homogenous parabolic partial differential equation

Methods and Formulation

Results and Discussions 7

Conclusion