Abstract
A mixed problem with simple boundary conditions is considered for the two-dimensional wave-operator and for the corresponding system of first order equations. Some particular difference approximations to the problem are studied, and their stability and convergence are proved by means of energy inequalities, when the mesh ratio satisfies certain necessary and sufficient conditions. The case of variable coefficients and additional lower order terms is also covered.
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Friberg, J. Conditionally stable difference approximations for the wave-operator. BIT 1, 69–86 (1961). https://doi.org/10.1007/BF01939220
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DOI: https://doi.org/10.1007/BF01939220