Numerical Solution of Seventh-Order Boundary Value Problems by a Novel Method

We demonstrate the efficiency of reproducing kernel Hilbert space method on the seventh-order boundary value problems satisfying boundary conditions. These results have been compared with the results that are obtained by variational iteration method (VIM), homotopy perturbation method (HPM), Adomian decomposition method (ADM), variation of parameters method (VPM), and homotopy analysis method (HAM). Obtained results show that our method is very effective

Approximate Solution of Second-Order Integrodifferential Equation of Volterra Type in RKHS Method

Abstract In this paper, an application of reproducing kernel Hilbert space (RKHS) method is applied to solve second-order integrodifferential equation of Volterra type. The analytical solution is represented in the form of series in the reproducing kernel space. The n−truncation approximation u n (x) is obtained and proved to converge to the analytical solution u(x). Moreover, the presented method has an advantages that it is possible to pick any point in the interval domain and as well the approximate solution and its derivatives will be applicable Numerical experiments are displayed to illustrate the validity, accuracy, efficiency and applicability of the proposed method. Results indicates that our technique is simple, straightforward and effective. Mathematics Subject Classification: 47B32, 45J05, 34K2

New Reproducing Kernel Functions

Some new reproducing kernel functions on time scales are presented. Reproducing kernel functions have not been found on time scales till now. These functions are very important on time scales and they will be very useful for researchers. We need these functions to solve dynamic equations on time scales with the reproducing kernel method