Second derivative methods with RK stability. (English) Zbl 1084.65069

Authors’ summary: General linear methods are extended to the case in which second derivatives, as well as first derivatives, can be calculated. Methods are constructed of third and fourth order which are A-stable, possess the Runge-Kutta (RK) stability property and have a diagonally implicit structure for efficient implementation.
Reviewer’s remark: Such methods are at an early stage of devlopment but the present results, and the fact that there is a fair amount of freedom in choosing method parameters, show these methods deserve further development. The issues of starting procedure, error estimation, and stepsize control remain to be addressed.


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