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.
In this paper, an application of reproducing kernel Hilbert space (RKHS) method is applied to solve system of Fredholm integro-differential equations. The exact solutions are represented in the form of series in the reproducing kernel space. Moreover, the approximate solutions u n (x), v n (x) are proved to converge to the exact solutions u(x), v(x), respectively. The results reveal that the RKHS is simple and effective.
New class of spaces is introduced in this paper as a generalization of countably compact spaces called nearly countably compact spaces. Some characterizations and results about this new class of spaces are also presented. We give a definition of more generalized kind of spaces and we call it nearly regular countably compact spaces. Also, we study the effect of some mappings on the nearly countably compact spaces.
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