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Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space. (English) Zbl 1193.34017

Summary: We present a new method for solving a singular nonlinear second-order periodic boundary value problem. Its analytical solution is represented in the form of series in the reproducing kernel space. In the mean time, the \(n\)-term approximation \(u_n(x)\) to the analytical solution \(u(x)\) is obtained and is proved to converge to the analytical solution. Some numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method indicate the method is simple and effective.

MSC:

34A45 Theoretical approximation of solutions to ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
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References:

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