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De Meyer, H.; Van Hecke, T.; Vanden Berghe, G.; Van Daele, M.

Multistride \(L\)-stable fourth-order methods for the numerical solution of ODEs. (English) Zbl 0866.65052

Comput. Math. Appl. 32, No. 7, 1-8 (1996).
Summary: Recently, M. M. Chawla, A. A. Karaballi and M. S. Al-Sahhar [Extended double-stride \(L\)-stable methods for the numerical solution of ODEs. Comput. Math. Appl. 31, No. 2, 1-6 (1996)] have obtained a one-parameter family of double-stride \(L\)-stable methods of fourth order by the coupling of three linear multistep methods. Here we present an alternative derivation technique based on mono-implicit Runge-Kutta (MIRK) methods. The MIRK method provides a framework within which all families of double- and triple-stride \(L\)-stable methods of fourth order can be expressed. The well-established theory for Runge-Kutta methods can then be used to derive these families in a straightforward manner.

Cited in 2 Documents

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L20 Stability and convergence of numerical methods for ordinary differential equations

Keywords:

\(L\)-stability; \(A\)-stability; Simpson’s rule; mono-implicit Runge-Kutta methods; double-stride \(L\)-stable methods; linear multistep methods
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References:

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