Numerical Scheme based on Non-polynomial Spline Functions for ‎the System of Second Order Boundary Value Problems arising in ‎Various Engineering Applications

Several applications of computational science and engineering, including population dynamics, optimal control, and physics, reduce to the study of a system of second-order boundary value problems. To achieve the improved solution of these problems, an efficient numerical method is developed by using spline functions. A non-polynomial cubic spline-based method is proposed for the first time to solve a linear system of second-order differential equations. Convergence and stability of the proposed method are also investigated. A mathematical procedure is described in detail, and several examples are solved with numerical and graphical illustrations. It is shown that our method yields improved results when compared to the results available in the literature.

Keywords:

Linear System , Second-order boundary-value problems , Numerical approximation , Cubic non-polynomial spline , Convergence ‎analysis , Error analysis‎