Reproducing Kernel method for the solution of nonlinear hyperbolic telegraph equation with an integral condition |
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Authors: | Huanmin Yao |
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Institution: | School of Mathematics and Sciences, Harbin Normal University, Harbin, Heilongjiang 150025, China |
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Abstract: | In this article, an iterative method is proposed for solving nonlinear hyperbolic telegraph equation with an integral condition. Its exact solution is represented in the form of series in the reproducing kernel space. In the mean time, the n‐term approximation un(x, t) of the exact solution u(x, t) is obtained and is proved to converge to the exact solution. Moreover, the partial derivatives of un(x, t) are also convergent to the partial derivatives of u(x, t). Some numerical examples have been studied to demonstrate the accuracy of the present method. Results obtained by the method have been compared with the exact solution of each example and are found to be in good agreement with each other. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 867–886, 2011 |
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Keywords: | approximate solution hyperbolic telegraph equation integral conditions iterative sequence reproducing kernel space |
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