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Time-point relaxation Runge-Kutta methods for ordinary differential equations. (English) Zbl 0783.65063

Time-point relaxation Runge-Kutta methods are implemented in Gauss-Jacobi and Gauss-Seidel modes. The authors show that if the number of Picard- Lindelöf iterations tends to infinity, then these modes tend to the same one-step method for ordinary differential equations called diagonal split Runge-Kutta method. The convergence order and the stability regions are investigated in detail.

MSC:

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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