New fourth-order splitting methods for two-dimensional evolution equations

N. V. Shirobokov

Southern Ural State University, pr. Lenina 76, Chelyabinsk, 454080, Russia

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.

Key words: two-dimensional evolution equations, Runge–Kutta methods, diagonal implicit methods, stiff problems, splitting methods, Burgers' equation.

UDC: 519.63

Received: 29.03.2008

 English version: Computational Mathematics and Mathematical Physics, 2009, 49:4, 672–675

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