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Rosenbrock-type ‘peer’ two-step methods. (English) Zbl 1072.65107
The authors construct \(s\)-stage methods for solving initial value problems for stiff ordinary differential equations where all stage values have stage order \(s-1.\) The proposed class of methods is stable in the sense of zero-stability for arbitrary stepsize sequences. Using the concept of effective order the authors derive methods having order \(s\) for constant stepsizes.

MSC:
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65Y05 Parallel numerical computation
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
Software:
ROS3P
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References:
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