Analytical simulation of singular second-order, three points boundary value problems for fredholm operator using computational kernel algorithm

A numerical algorithm for solving second-order, three-point singular boundary value problems restricted by Fredholm operator is presented in favorable reproducing kernel Hilbert spaces. The analytical-numerical solutions of the problems are given with series form in the Hilbert space W3 2 [0,1] with easily computable components using Maple 13 software package. In finding the analytical-numerical solutions, we use generating the orthogonal basis from the obtained kernel functions such that the orthonormal basis is constructing in order to formulate and utilize the solutions. Numerical experiments are carried where two smooth reproducing kernel functions are used throughout the evolution of the algorithm to obtain the required nodal values of the unknown variables. Several computational simulation experiments are given to show the good performance of the proposed procedure. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to multipoint singular boundary value problems restricted by Fredholm operators.