Solving system of second-order BVPs using a new algorithm based on reproducing kernel Hilbert space

Abstract

In this study, a new and reliable technique based on Reproducing Kernel Method (RKM) is introduced to solve the linear and nonlinear system of second-order boundary value problem. We propose that RKM without Gram-Schmidt orthogonalization process significantly reduces the CPU time and increases the accuracy of the approximate solutions. The convergence theorem and error analysis are also verified. An algorithm is presented to indicate the steps of implementing the proposed scheme. Since the system of second-order boundary value problem is solvable with the numerical commands in Mathematica software, we examined these commands for numerical examples, compared the results with the present method, and demonstrated the higher precision of the present algorithm.