A new algorithm for a class of singular boundary value problems

A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method

“…Geng and Cui [16] applied the RKHSM to handle the second-order boundary value problems. Yao and Cui [17] and Wang et al [18] investigated a class of singular boundary value problems by this method and the obtained results were good. Zhou et al [19] used the RKHSM effectively to solve second-order boundary value problems.…”

A new method for solving singular fourth-order boundary value problems with mixed boundary conditions

“…In [1][2][3][4][5][6][7][8], it is very difficult to get reproducing kernel space of problem (1). This paper is concerned with a new algorithm for giving the analytical and approximate solutions of a class of fourth-order in the new reproducing kernel space.…”

“…Many authors [9][10][11][12][13][14][15] have studied existence and uniqueness of fourth order ordinary differential equations with various boundary conditions. Recently, the reproducing kernel methods [1][2][3][4][5][6][7][8] emerge one after another. However, these reproducing kernel methods are very difficult to deal with the general conditions of determining the solution.…”

A new method for solving a class of mixed boundary value problems with singular coefficient

“…In [1][2][3][4][5][6][7], it is very difficult to deal with initial boundary value conditions. In this paper, we give a new method to deal with boundary value conditions, the main contribution of this paper is to put mixed boundary value conditions into reproducing kernel Hilbert space.…”