Applied Mathematics & Information Sciences

Author Country (or Countries)

Saudi Arabia


The aim of the present analysis is to implement a relatively recent computational method, the reproducing kernel Hilbert space, for obtaining numerical solutions for differential algebraic system of integral-initial conditions. Two extended inner product spaces W [0, 1] and H [0, 1] are constructed in which the integral-initial conditions of the systems are satisfied. Whilst, two smooth kernel functions Rt (s) and rt (s) are used throughout the evolution of the algorithm in order to obtain the required grid points. 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. In this approach, computational results of some numerical examples are presented to illustrate the viability, simplicity, and applicability of the algorithm developed. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to such systems.

Digital Object Identifier (DOI)