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Richardson extrapolation combined with the sequential splitting procedure and the \(\theta \)-method. (English) Zbl 1250.65097

The authors use the Richardson extrapolation to solve numerically the initial value problem for a system of differential equations of the form \[ y'(t) = f_{1}(t,y)+f_{2}(t,y),\qquad t\in [a,b],\qquad y(a)=y_{0}. \] The approximate solution is obtained using the weighted average with the parameter \(\theta\), evaluated in the points \(t_{n-1}\) and \( t_{n-\frac{1}{2}}\). The stability of this method is proved using the stability function \( R(\mu)\).

MSC:

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
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations

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References:

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