Numerical integrators for stiff and highly oscillatory differential equations

Author:
Simeon Ola Fatunla

Journal:
Math. Comp. **34** (1980), 373-390

MSC:
Primary 65L05

MathSciNet review:
559191

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Abstract: Some *L*-stable fourth-order explicit one-step numerical integration formulas which require no matrix inversion are proposed to cope effectively with systems of ordinary differential equations with large Lipschitz constants (including those having highly oscillatory solutions). The implicit integration procedure proposed in Fatunla [11] is further developed to handle a larger class of stiff systems as well as those with highly oscillatory solutions. The same pair of nonlinear equations as in [11] is solved for the stiffness/oscillatory parameters. However, the nonlinear systems are transformed into linear forms and an efficient computational procedure is developed to obtain these parameters. The new schemes compare favorably with the backward differentiation formula (DIFSUB) of Gear [13], [14] and the blended linear multistep methods of Skeel and Kong [24], and the symmetric multistep methods of Lambert and Watson [17].

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1980-0559191-X

Keywords:
Stiffness and oscillatory parameters,
ordinary differential equations,
*L*-stable,
eigenvalues,
meshsize,
explicit,
implicit,
*A*-stable,
exponential fitting

Article copyright:
© Copyright 1980
American Mathematical Society