A smooth approximation for the solution of special non-linear third-order boundary-value problems based on non-polynomial splines

Abstract

A second-order method based on quartic non-polynomial spline consisting of a polynomial part of degree two and a trigonometric part is developed to find continuous approximation of a two point boundary-value problem involving a third-order differential equation. It is shown that the angular frequency k of the trigonometric part can be used to raise the order of accuracy of the new scheme. Convergence of the method is shown along with numerical examples each for linear and non-linear cases to demonstrate the practical usefulness of the new method. Comparison with existing methods of the same order is given to exhibit superiority of the method.

Keywords:

• Third-order boundary-value problems
• Non-polynomial splines
• Quartic splines
• Convergence