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# Convergence of a Second-Order Scheme for Semilinear Hyperbolic Equations in $2 + 1$ Dimensions

Robert Glassey and Jack Schaeffer
Mathematics of Computation
Vol. 56, No. 193 (Jan., 1991), pp. 87-106
DOI: 10.2307/2008531
Stable URL: http://www.jstor.org/stable/2008531
Page Count: 20
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## Abstract

A second-order energy-preserving scheme is studied for the solution of the semilinear Cauchy Problem $u_{tt} - u_{xx} - u_{yy} + u^3 = 0 (t > 0; x, y \in \Bbb{R})$. Smooth data functions of compact support are prescribed at $t = 0$. On any time interval $\lbrack0, T\rbrack$, second-order convergence (up to logarithmic corrections) to the exact solution is established in both the energy and uniform norms.

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