Optimal finite difference schemes for the wave equation
A. F. Mastryukov
Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Acad. Lavrentieva 6, Novosibirsk, 630090, Russia
Keywords: волновое уравнение, электромагнитные волны, конечно-разностный метод, оптимальный, точность, метод Лагерра, система линейных уравнений, итерации, wave equation, electromagnetic wave, finite-difference, optimal, accuracy, Laguerre method, linear system of equations
Abstract
This paper considers the solution of the two-dimensional wave equation with the use of the Laguerre transform. The optimal parameters of finite difference schemes for this equation have been obtained. Numerical values of these optimal parameters are specified. The finite difference schemes of second order with optimal parameters give the accuracy of the solution to the equations close to the accuracy of the solution by the scheme of fourth order. It is shown that using the Laguerre decomposition, the number of optimal parameters in comparison with the Fourier decomposition can be reduced. This reduction leads to simplification of finite difference schemes and to reduction of the number of computations, i.e. the efficiency of the algorithm.
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