Numerical scheme based on non-polynomial spline functions for the system of second order ...

Several applications of computational science and engineering including population dynamics, optimal control and physics, etc. reduces to the study of system of second order boundary value problems. To achieve the improved solution of these problems, we develop an efficient numerical method by using spline functions. 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. Mathematical procedure is described in detail and several examples are solved with the numerical and graphical illustrations. It is shown that our method yields improved results when compared with the results available in the literature.