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Reproducing Kernel method for the solution of nonlinear hyperbolic telegraph equation with an integral condition
Author(s) -
Yao Huanmin
Publication year - 2011
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20558
Subject(s) - mathematics , kernel (algebra) , hyperbolic partial differential equation , partial differential equation , mathematical analysis , exact solutions in general relativity , series (stratigraphy) , telegrapher's equations , nonlinear system , integral equation , partial derivative , iterative method , space (punctuation) , convergent series , pure mathematics , mathematical optimization , paleontology , linguistics , physics , philosophy , quantum mechanics , electrical engineering , electric power transmission , biology , engineering , power series
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 u n ( 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 u n ( 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