On the numerical integration of orthogonal flows with Runge-Kutta methods (Q1971821)
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scientific article; zbMATH DE number 1423313
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the numerical integration of orthogonal flows with Runge-Kutta methods |
scientific article; zbMATH DE number 1423313 |
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On the numerical integration of orthogonal flows with Runge-Kutta methods (English)
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7 June 2000
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The paper deals with the numerical solution of an initial value problem for matrix differential equations of special form (that preserves orthogonality of the flows) by some implicit Runge-Kutta methods based on Gauss-Legendre quadrature (named GLRK methods). The stability and convergence properties of linearly implicit orthogonal methods are proved. Orthogonal methods of orders 3 and 4 based on two-stage GLRK methods combined with suitable explicit Runge-Kutta schemes are presented. Numerical experiments are performed.
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initial value problems
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implicit Runge-Kutta methods
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orthogonal flows
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matrix differential equations
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stability
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convergence
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linearly implicit orthogonal methods
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numerical experiments
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