Numerical Solution of The Seventh Order Boundary Value Problems using B-spline Method

TL;DR

This paper introduces a B-spline based numerical method for solving seventh order boundary value problems, demonstrating high accuracy and effectiveness through example applications.

Contribution

The paper develops a septic B-spline collocation method specifically for seventh order boundary value problems, which is a novel application of B-splines.

Findings

High accuracy with low absolute errors

Effective for high order boundary value problems

Agreement between approximate and exact solutions

Abstract

We develop a numerical method for solving the boundary value problem of The Linear Seventh Ordinary Boundary Value Problem by using seventh degree B-Spline function. Formulation is based on particular terms of order of seventh order boundary value problem. We obtain Septic B-Spline formulation and the Collocation B-spline Method is formulated as an approximation solution. We apply the presented method to solve an example of seventh-order boundary value problem which the results show that there is an agreement between approximate solutions and exact solutions. Resulting low absolute errors show that the presented numerical method is effective for solving high order boundary value problems. Finally, a general conclusion has been included.