Nonpolynomial twin parameter spline approach to treat boundary-value problems arising in engineering problems

Abstract

This study puts forward construction of an efficient nonpolynomial twin parameter cubic spline-based numerical scheme for approximations to the solution of heat transfer and defection in cables problems represented as system of second-order boundary-value problems. The introduction of an additional parameter in trigonometric part of nonpolynomial cubic spline makes this scheme a better one as compared to other existing numerical methods. The Icing on the cake is the applicability of the proposed scheme for unequal step size. The present algorithm gives better approximations in comparison to other spline, collocation, and finite-difference methods. The convergence analysis of the proposed algorithm is talked about to make a strong foundation to the proposed algorithm. Practical usefulness of the proposed method is illustrated through numerical examples.