A new fourth-order compact finite difference scheme for the two-dimensional second-order hyperbolic equation

Authors:
Hengfei Ding;Yuxin Zhang
Affiliations:
School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, PR China;School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this paper, we propose a three level compact difference scheme of O(@t^4+h^4) for the difference solution of a two-dimensional second-order non-homogeneous linear hyperbolic equation u"t"t+2@au"t+@b^2u=u"x"x+u"y"y+f(x,y,t),00, where @a@b=0. Stability analysis of the method has been carried out. Finally, numerical examples are used to illustrate the efficiency of the new difference scheme.