Efficient and accurate numerical methods for nonlinear strongly damped wave equation in 2+1 dimensions.

In this article, two difference schemes are proposed to solve numerically a nonlinear strong damped wave equation in two dimensions. The first scheme is nonlinear implicit, the second scheme is linear implicit. It is proved that the two schemes are unique solvable, unconditionally stable. Moreover, the present numerical methods are convergent with second order accuracy both in space and time in the discrete H 1 -norm. Numerical experiments are provided to show the validity and the accuracy of the proposed difference schemes as well as their efficiency. [ABSTRACT FROM AUTHOR]