Approximate Solutions of DASs with Nonclassical Boundary Conditions using Novel Reproducing Kernel Algorithm

Abstract

This paper presents novel reproducing kernel algorithm for obtaining the numerical solutions of differential algebraic systems with nonclassical boundary conditions for ordinary differential equations. The representation of the exact and the numerical solutions is given in the W [0, 1] and H [0, 1] inner product spaces. The computation of the required grid points is relying on the R_t (s) and r_t (s) reproducing kernel functions. An efficient construction is given to obtain the numerical solutions for the systems together with an existence proof of the exact solutions based upon the reproducing kernel theory. Numerical solutions of such nonclassical systems are acquired by interrupting the η-term of the exact solutions. In this approach, numerical examples were analyzed to illustrate the design procedure and confirm the performance of the proposed algorithm in the form of tabulate data and numerical comparisons. Finally, the utilized results show the significant improvement of the algorithm while saving the convergence accuracy and time.