This paper is concerned with a technique for solving Fredholm integro-dierentialequations in the reproducing kernel Hilbert space. In contrast with the conventionalreproducing kernel method, the Gram-Schmidt process is omitted hereand satisfactory results are obtained. The analytical solution is represented inthe form of series. An iterative method is given to obtain the approximate solution.Th...

This paper investigates the analytical approximate solutions of singular fourth order four-point boundary value problems using reproducing kernel method (RKM). The solution obtained by using the method takes the form of a convergent series with easily computable components. However, the reproducing kernel method can not be used directly to solve singular fourth order four-point boundary value p...

Summary The performance of adaptive estimators that employ embedding in reproducing kernel Hilbert spaces (RKHS) depends on the choice location basis centers. Parameter convergence and error approximation rates depend where how centers are distributed state‐space. In this article, we develop theory relates parameter to position We criteria for choosing a specific class systems by exploiting fac...

In this paper, we present a new method for solving Reproducing Kernel Space (RKS) theory, and iterative algorithm for solving Generalized Burgers Equation (GBE) is presented. The analytical solution is shown in a series in a RKS, and the approximate solution u(x,t) is constructed by truncating the series. The convergence of u(x,t) to the analytical solution is also proved.