New algorithm for second-order boundary value problems of integro-differential equation

Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations

“…(1) subject to the periodic boundary conditions (2) has a unique solution on ½0; 1. But on the other aspect as well, the numerical solvability of IDEs of different types and orders can be found in [17][18][19][20][21] and references therein. Also, for numerical solvability of different categories of two-point, second-order BVPs one can consult the Refs.…”

“…The RKHS method was used by many authors to investigate several scientific applications side by side with their theory. The reader is kindly requested to go through [18][19][20][21][24][25][26][27][28][29][30][31][32][33][34][35][36] in order to know more details about RKHS method, including its history, its modification for use, its applications, its iterative property, and its characteristics.…”

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.…”