Quintic Spline Solutions of Fourth Order Boundary-Value Problems

TL;DR

This paper introduces a quintic spline method for numerically solving fourth order linear boundary-value problems, providing a new approach with derived end conditions and demonstrating its effectiveness through numerical examples.

Contribution

The paper develops a novel quintic spline technique with specific end conditions for fourth order boundary-value problems, enhancing numerical solution accuracy.

Findings

Effective approximation of solutions and derivatives

Numerical results demonstrate practical usefulness

Method improves solution accuracy for boundary-value problems

Abstract

In this paper Quintic Spline is defined for the numerical solutions of the fourth order linear special case Boundary Value Problems. End conditions are also derived to complete the definition of spline.The algorithm developed approximates the solutions, and their higher order derivatives of differential equations. Numerical illustrations are tabulated to demonstrate the practical usefulness of method.