Constructing of linearly implicit schemes which are LN-equivalent to implicit Runge–Kutta methods

Zubanov A.M., Kutruhin N.N., Shirkov P.D.
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New family of linearly implicit schemes are presented. This family allows to obtain methods which are equivalent to stiffly accurate implicit Runge–Kutta schemes (such as RadauIIA and LobattoIIIC) on nonautonomous linear problems. Notion of LN-equivalence of schemes is introduced. Order conditions and stability conditions of such methods are obtained with the use of media for computer symbolic calculations. Some examples of new schemes have been constructed. Numerical studying of new method have been done with the use of classical tests for stiff problems.

Keywords: stiff systems of ordinary differential equations, stiffly accurate Runge–Kutta methods and Rosenbrock schemes, stability and L-equivalence
Citation in English: Zubanov A.M., Kutruhin N.N., Shirkov P.D. Constructing of linearly implicit schemes which are LN-equivalent to implicit Runge–Kutta methods // Computer Research and Modeling, 2012, vol. 4, no. 3, pp. 483-496
Citation in English: Zubanov A.M., Kutruhin N.N., Shirkov P.D. Constructing of linearly implicit schemes which are LN-equivalent to implicit Runge–Kutta methods // Computer Research and Modeling, 2012, vol. 4, no. 3, pp. 483-496
DOI: 10.20537/2076-7633-2012-4-3-483-496
URL: http://crm-en.ics.org.ru/journal/article/1918/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.
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