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