An Explicit Method for Numerical Simulation of Wave Equations

Abstract eng:
A method to develop a hierarchy of explicit recursion formulas for numerical simulation in irregular grids for scalar wave equations is presented and then is used to construct the formulas for the one-dimensional case in this paper. Numerical simulation of the one-dimensional scalar wave equation in a regular grid is discussed for understanding its accuracy and stability, and an approach is then proposed to construct the stable formulas which are of 2M-order of accuracy both in time and space with M being a positive integer and the recursion formulas of the second order (M=1) and the fourth order (M=2) are given as an example. Theoretical results of the method are demonstrated by a series of numerical tests.

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