Computational Approach for Fourth-Order Self-Adjoint Singularly Perturbed Boundary Value Problems via Non- polynomial Quintic Spline

摘要

This paper proposes a non-polynomial quintic spline method for approximate solutions of fourth-order self-adjoint singular perturbation boundary value problems, which comprises the polynomial part of degree three and two non-polynomial terms, i.e., sine and cosine. It is explicitly shown that the free parameter $$tau$$ τ of the non-polynomial part can be used to raise the order of accuracy of the scheme. The method has been proved for the second and fourth-order convergence. The proposed scheme is tested on two examples. The experimental results are compared with the existing method.