论文信息 - Second order Chebyshev methods based on orthogonal polynomials

Second order Chebyshev methods based on orthogonal polynomials

Summary. Stabilized methods (also called Chebyshev methods) are explicit Runge-Kutta methods with extended stability domains along the negative real axis. These methods are intended for large mildly stiff problems, originating mainly from parabolic PDEs. The aim of this paper is to show that with the use of orthogonal polynomials, we can construct nearly optimal stability polynomials of second order with a three-term recurrence relation. These polynomials can be used to construct a new numerical method, which is implemented in a code called ROCK2. This new numerical method can be seen as a combination of van der Houwen-Sommeijer-type methods and Lebedev-type methods.

Assyr Abdulle | Alexei A. Medovikov | A. Abdulle | A. Medovikov

[1] L. Shampine,et al. RKC: an explicit solver for parabolic PDEs , 1998 .

[2] P. Houwen,et al. On the Internal Stability of Explicit, m‐Stage Runge‐Kutta Methods for Large m‐Values , 1979 .

[3] J. Verwer. Explicit Runge-Kutta methods for parabolic partial differential equations , 1996 .

[4] E. B. Christoffel,et al. Über die Gaußische Quadratur und eine Verallgemeinerung derselben. , 1858 .

[5] A. Medovikov. High order explicit methods for parabolic equations , 1998 .

[6] Kjell Gustafsson,et al. Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods , 1991, TOMS.

[7] V. Lebedev,et al. Zolotarev polynomials and extremum problems , 1994 .