Novikov E.A.
Algorithm based on the L-stable (4,2) -method of the fourth order
The Rosenbrock methods obtained a wide circulation on solving stiff problems [1]. These schemes are obtained from semi-implicit methods of the Runge-Kutta type, which use one iteration of the Newton method. Accuracy of calculations is promoted by choosing an appropriate integration step. The maximal accuracy order of such methods with freezing the Jacobi matrix is 2, that limits its use to solving problems of low dimensions. There is the class of (m,k)-methods suggested in [2], which implementation is simple too, but for which the problem of freezing is solved easy. In this paper the L-stable (4,2)-method of the fourth order is constructed. The way of order conditions linearization is suggested. The inequality for accuracy control is obtained using an embedded method and the alternating step algorithm is formulated. Numerical results of the Ring modulator simulation are given. This work was partially supported by Russian foundation for basic research (project code 14-01-00047).
1. Rosenbrock H.H. Some general implicit processes for the numerical solution of differential equations // Computer. 1963. Vol. 5. P. 329–330.
2. Novikov E.A., Shitov Yu. A., Shokin Yu. I. One-step non-iterative methods for solving stiff problems // Contributions of Academy of Sciences of USSR. 1988. Vol. 301, №6. P. 1310-1314.
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