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Convergence of a second-order scheme for semilinear hyperbolic equations in $ 2+1$ dimensions

Authors: Robert Glassey and Jack Schaeffer
Journal: Math. Comp. 56 (1991), 87-106
MSC: Primary 65M12; Secondary 35L70
MathSciNet review: 1052095
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Abstract: A second-order energy-preserving scheme is studied for the solution of the semilinear Cauchy Problem $ {u_{tt}} - {u_{xx}} - {u_{yy}} + {u^3} = 0\;(t > 0;x,y \in \mathbb{R})$. Smooth data functions of compact support are prescribed at $ t = 0$. On any time interval [0, T], second-order convergence (up to logarithmic corrections) to the exact solution is established in both the energy and uniform norms.

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Article copyright: © Copyright 1991 American Mathematical Society