Mathematical foundations and some applications of the reproducing kernel method

This thesis is organized in eight sections. In Section 1, information about the history of the reproducing kernel method is presented. In Section 2, some fundamental definitions and theorems are introduced. In Section 3, some basic definitions and theorems of the reproducing kernel method are given. In Section 4, solution of the sine--Gordon equation is acquired by the reproducing kernel Hilbert space method. In Section 5, solution of the Bratu problem is found by the reproducing kernel Hilbert space method. In Section 6, solution of the MHD squeezing fluid flow is given by the reproducing kernel Hilbert space method. In Section 7, solutions of seventh order boundary value problems are presented by the reproducing kernel Hilbert space method. In Section 8, results and discussion are given.