The Convergence and Stability of Splitting Finite-Difference Schemes for Nonlinear Evolutionary Equations |
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| Authors: | M Radziunas F Ivanauskas |
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| Institution: | (1) Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany;(2) Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania;(3) Institute of Mathematics and Informatics, Akademijos 4, LT-08663 Vilnius, Lithuania |
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| Abstract: | We consider a splitting finite-difference scheme for an initial-boundary value problem for a two-dimensional nonlinear evolutionary
equation. The problem is split into nonlinear and linear parts. The linear part is also split into locally one-dimensional
equations. We prove the convergence and stability of the scheme in L
2 and C norms.
Printed in Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 413–434, July–September, 2005. |
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| Keywords: | finite-difference scheme locally one-dimensional scheme splitting method nonlinear evolutionary equation convergence stability |
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