Zlatev, Zahari; Faragó, István; Havasi, Ágnes Richardson extrapolation combined with the sequential splitting procedure and the \(\theta \)-method. (English) Zbl 1250.65097 Cent. Eur. J. Math. 10, No. 1, 159-172 (2012). 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 \( R(\mu)\). Reviewer: Ivan Secrieru (Chişinău) Cited in 7 Documents 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 Keywords:Cauchy problem; weighted scheme of quadrature formulas; Richardson extrapolation rule; system; stability Software:LAPACK; CLAPACK PDFBibTeX XMLCite \textit{Z. Zlatev} et al., Cent. Eur. J. Math. 10, No. 1, 159--172 (2012; Zbl 1250.65097) Full Text: DOI References: [1] Anderson E., Bai Z., Bischof C., Demmel J., Dongarra J., Du Croz J., Greenbaum A., Hammarling S., McKenney A., Ostrouchov S., Sorensen D., LAPACK: Users’ Guide, SIAM, Philadelphia, 1992; · Zbl 0843.65018 [2] Burrage K., Parallel and Sequential Methods for Ordinary Differential Equations, Numer. Math. Sci. 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