Solving a class of linear nonlocal boundary value problems using the reproducing kernel

New Spline Method for Solving Linear Two-Point Boundary Value Problems

“…Spectral method gives highly accurate solutions to boundary value problems [7]. Reproducing kernel gives quite accurate and efficient solution for linear fourth-order multi-point boundary value problems [8,9]. Finite difference method gives highly accurate results only at the chosen knots whereas in some other methods, the results can be obtained at any point in the domain [3,15].…”

Using Reproducing Kernel for Solving a Class of Fractional Order Integral Differential Equations

“…However, it is very difficult to obtain the analytic solution of linear integrodifferential equations of fractional order, so many researchers try their best to study numerical solution of linear FIDEs and system of linear FIDEs in recent years [1][2][3][4][5]. Since the reproducing kernel method can not only obtain the exact solution in the form of series but also obtain the approximate solution with higher accuracy, the method has been widely used in linear and nonlinear problems, integral and differential equations, fractional partial differential equation, and so on [6][7][8][9][10][11][12][13][14][15]. But there are no scholars that use the reproducing kernel interpolation collocation method to solve the linear integrodifferential equations of fractional order.…”

Reproducing kernel method to solve parabolic partial differential equations with nonlocal conditions

“…Obtaining the reproducing kernel such that satisfies the nonlocal conditions is very important to the considered problem. For this purpose, we use the idea that was first presented by Wang et al [16][17][18]. To achieve this goal, we must first construct reproducing kernel spaces and their kernels such that satisfy the nonlocal conditions, and then implement RKM without Gram-Schmidt orthogonalization process on the problem (1).…”