POLYNOMIAL CUBIC SPLINE METHOD FOR SOLVING FOURTH-ORDER PARABOLIC TWO POINT BOUNDARY VALUE PROBLEMS

Abstract

Partial differential equations (PDEs) played a vital role in natural sciences and engineering. Different studies were carried out for solving fourth-order partial differential equations. These equations governed the oblique vibrations of a uniform beam. This study presented and illustrated a new technique for the numerical approximations of fourth-order partial differential equations (PDEs). The new technique was based on the fact of employing polynomial cubic spline method (PCSM) along with the Adomian decomposition method (ADM). The Adomian decomposition method was used to obtain the boundary conditions for the replaced variables, whereas continuous approximation was constructed and applied on the decomposed system of PDEs. The performance of the developed scheme was illustrated by numerical tests that involved numerical approximations with the exact solutions on a collection of test problems.