An iterative method for solving fourth-order boundary value problems of mixed type integro-differential equations

作者：Abu Arqub Omar^*

来源：Journal of Computational Analysis and Applications, 2015, 18(5): 857-874.

• Integro-differential equation
• Reproducing kernel function
• Iterative method

In this paper, reproducing kernel Hilbert space method is introduced as an efficient solver for fourth-order boundary value problems of mixed type integro-differential equations where two reproducing kernel functions are used throughout the evolution of the algorithm to obtain the required nodal values of the unknown variable. The solution methodology is based on generating the orthogonal basis from the obtained kernel function in the space W-2(5) [0, 1]. After that, the orthonormal basis is constructing in order to formulate and utilize the solution in the same space. In addition to that, an error estimation and bound based on the use of reproducing kernel theory has been carried out. Four numerical test problems including linear and nonlinear equations were analyzed to illustrate the procedure and confirm the performance of the proposed method. The numerical results show that the proposed algorithm is a robust and accurate procedure for solving fourth-order boundary value problems of mixed type integro-differential equations.

• 出版日期2015-5