In this paper, we study the Legendre spectral element method for solving the sine-Gordon equation in one dimension. Firstly, we discretize the equation by Legendre spectral element in space and then discretize the time by the second-order leap-frog method. We study the stability and convergence of the method and show the convergence of our method. Finally, we show the results with numerical examples.
MSC: 65M70; 65M06; 74G15
In this paper we present a computational technique for solving the second-order Fredholm integro-differential equations. The method is based on a non-classical pseudospectral method. The differential matrices are computed and are utilized to reduce the second-order Fredholm integro-differential equations to algebraic equations. Numerical examples are presented to demonstrate the validity and applicability of the new method.
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