Efficient algorithms for fourth and sixth-order two-point non-linear boundary value problems using non-polynomial spline approximations on a geometric mesh

Abstract

An efficient algorithm for the numerical solution of linear and non-linear higher (even)-order two-point boundary value problems has been developed. The method is third-order accurate and applicable to both singular and non-singular cases. We have used non-polynomial spline basis and geometric mesh finite differences for the generation of new scheme. The irreducibility and monotone property of the iteration matrix have been established, that justify the convergence property of the proposed method. Some computational experiments have been carried out to demonstrate the efficiency in terms of convergence order and maximum absolute error estimates. The numerical results justify the reliability and efficiency of the method both in terms of order and accuracy.