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    Finite difference method for the third-order partial differential equation with nonlocal boundary conditions
    (Maltepe Üniversitesi, 2019) Ashyralyev, Allaberen; Belakroum, Kheireddine
    The theory and applications of local and nonlocal boundary value problems for a third-order partial differential equations have been investigated widely in the literature. In the present work, we study the nonlocal boundary value problem, for third order partial differential equations in a Hilbert space H with a self-adjoint positive definite operator A.The main theorem on stability of this problem is established. The stability estimates for the solution of three problems for partial differential equations are obtained. Three-step difference schemes for the approximate solution of nonlocal boundary-value problem for the third-order partial differential equation are presented. Numerical experiments results are provided.
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    On the stability of nonlocal boundary value problem for a third order PDE
    (Maltepe Üniversitesi, 2019) Ashyralyev, Allaberen; Belakroum, Kheireddine
    In the present paper, we study the nonlocal boundary value problem for third order partial differential equations in a Hilbert space with a self-adjoint positive definite operator. The main theorem on stability of this problem is established. In Applications, stability estimates for the solution of two problems for third order partial differential equations are obtained.
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    Sinc approximation of solution of integro-differential equation
    (Maltepe Üniversitesi, 2019) Belakroum, Kheireddine; Belakroum, Dounia
    Many mathematical models of complex processes may be posed as integro-differential equations. Different numerical methods have been proposed and developed in recent years, such as quadrature method, collocation method, Galerkin method, expansion method and product-integration method. The application of the Sinc-Galerkin method to an approximate solution of integro-differential equations were discussed in this study. The method is based on approximating functions and their derivatives by using the Whittaker cardinal function in order to determine the approximate solutions. Without any numerical integration, the partial differential equation transformed to an algebraic equation system. For the numerical calculations, Maple is used and the results determined from the method are compared with the exact solutions. The results are illustrated both in table and graphically to show the rapid convergence and exceptional accuracy of the method.