APPLICATION OF REPRODUCING KERNEL ALGORITHM FOR SINGULAR BVPs INVOLVING FREDHOLM-VOLTERRA OPERATOR

Abstract

This paper proposes asymptotically efficient algorithm for treating classes of singular boundary value problems involving Fredholm and Volterra operators associated with three-point boundary conditions.  The algorithm methodology is proposed based on the novel reproducing kernel Hilbert space (RKHS) method, which is used directly without employing linearization and perturbation.  The orthonormal system is generated in a favorable Hilbert space on a compact dense interval to expand the solution in Fourier series formula with accurately computable components.  Numerical examples of singular multipoint BVPs are performed to support the theoretical statements that acquired by interrupting the n-term of the exact solutions.  Besides, the results obtained indicate that the RK procedure is effective and competitive with a great capability in scientific and engineering applications.