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Reproducing kernel method for solving nonlinear differential-difference equations. (English) Zbl 1251.34080
Summary: On the basis of reproducing kernel Hilbert spaces theory, an iterative algorithm for solving some nonlinear differential-difference equations (NDDEs) is presented. The analytical solution is shown in a series form in a reproducing kernel space, and the approximate solution u n,m is constructed by truncating the series to m terms. The convergence of u n,m to the analytical solution is also proved. Results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such differential-difference problems.
MSC:
34K07Theoretical approximation of solutions of functional-differential equations
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)