Solving third-order boundary value problems with quartic splines.

P K Pandey

doi:10.1186/s40064-016-1969-z

Abstract

In this article, we present a novel second order numerical method for solving third order boundary value problems using the quartic polynomial splines. We establish the convergence of the method. We present numerical experiments to demonstrate the efficiency of the method and validity of our second order method, which shows that present method gives better results.

Highlights

In this article we consider a quartic splines method for the numerical solution of the third order boundary value problems given as u′′′(x) = f (x, u), a ≤ x ≤ b, (1)
The emphasis in this article will be on the development of an efficient numerical method to deal with approximate numerical solution of the third order boundary value problem
We have described a numerical method for numerical solution of third order boundary value problem and three model problems including an obstacle problem considered to test the performance of the proposed method

Summary

Background

In this article we consider a quartic splines method for the numerical solution of the third order boundary value problems given as u′′′(x) = f (x, u), a ≤ x ≤ b,. The emphasis in this article will be on the development of an efficient numerical method to deal with approximate numerical solution of the third order boundary value problem. Some efficient and accurate numerical methods for solving higher order boundary value problems are available in literature. With advent of computers it gained important to develop more accurate numerical methods to solve higher order boundary value problems. The purpose of this article is to develop an efficient numerical method for solution of third order boundary value problems (1). We will consider following linear test equation for convergence analysis of the proposed method (7). We have used the following formula in computation of MAE,

Method

Conclusion