A Computational Method Based on Non-Polynomial Tension Splines for the Fourth-Order ODEs

Abstract

   In this study, a non-polynomial tension spline method is proposed for approximating the solution of fourth-order boundary value problems. The original fourth-order problem is reduced to an equivalent system of second-order problems, which is then solved using a mixed non-polynomial tension spline formulation. Numerical examples compared with exact solutions demonstrate the accuracy and efficiency of the proposed method.