Abstract
New second- and third-order splitting methods are proposed for partial differential equations of the evolution type in a two-dimensional space. The methods are derived as based on diagonal implicit techniques used in the numerical solution to stiff ordinary differential equations. The methods are absolutely and unconditionally stable. Test computations are presented.
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References
K. Dekker and J. G. Verwer, Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations (North-Holland, Amsterdam, 1984; Mir, Moscow, 1988).
N. V. Shirobokov, “Diagonally Implicit Runge-Kutta Methods,” Zh. Vychisl. Mat. Mat. Fiz. 42, 1012–1017 (2002) [Comput. Math. Math. Phys. 42, 974–979 (2002)].
N. V. Shirobokov, “New Splitting Methods for Two-Dimensional Evolutionary Equations,” Zh. Vychisl. Mat. Mat. Fiz. 47, 1187–1191 (2007) [Comput. Math. Math. Phys. 47, 1137–1141 (2007)].
G. I. Marchuk, Methods of Numerical Mathematics (Springer-Verlag, New York, 1975; Nauka, Moscow, 1980).
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Original Russian Text © N.V. Shirobokov, 2009, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2009, Vol. 49, No. 4, pp. 696–699.
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Shirobokov, N.V. New fourth-order splitting methods for two-dimensional evolution equations. Comput. Math. and Math. Phys. 49, 672–675 (2009). https://doi.org/10.1134/S0965542509040113
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DOI: https://doi.org/10.1134/S0965542509040113