New Runge-Kutta-Nyström formula-pairs of order 8(7), 9(8), 10(9) and 11(10) for differential equations of the form \(y=f(x,y)\)
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Publication:1063396
DOI10.1016/0377-0427(86)90073-7zbMath0574.65075OpenAlexW2067221458MaRDI QIDQ1063396
Publication date: 1986
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0377-0427(86)90073-7
Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05)
Related Items (22)
Embedded diagonally implicit Runge-Kutta-Nystrom 4(3) pair for solving special second-order IVPs ⋮ Continuous parallel-iterated RKN-type PC methods for nonstiff IVPs ⋮ Explicit symmetric Runge-Kutta-Nyström methods for parallel computers ⋮ Continuous extensions to Nyström methods for second order initial value problems ⋮ A new family of multistep numerical integration methods based on Hermite interpolation ⋮ Economical handling of Runge-Kutta-Nyström step rejection ⋮ High order explicit Runge-Kutta Nyström pairs ⋮ A new optimized non-FSAL embedded Runge-Kutta-Nyström algorithm of orders 6 and 4 in six stages ⋮ A general class of explicit pseudo--two-step RKN methods on parallel computers ⋮ Fast convergence pirkn-type pc methods with adams-type predictors∗ ⋮ A novel analytic continuation power series solution for the perturbed two-body problem ⋮ Twostep-by-twostep continuous PIRKN-type PC methods for nonstiff IVPs ⋮ Explicit pseudo two-step RKN methods with stepsize control ⋮ Explicit parallel two-step Runge-Kutta-Nyström methods ⋮ A variable step-size exponentially fitted explicit hybrid method for solving oscillatory problems ⋮ Scaled runge-kutta-nyström methods for the second order differential equationÿ=f(x,y) ⋮ Parallel block pc methods with rkn-type correctors and adams-type predictors∗ ⋮ Embedded implicit Runge–Kutta Nyström method for solving second-order differential equations ⋮ Explicit, high-order Runge-Kutta-Nyström methods for parallel computers ⋮ Two-step-by-two-step PIRKN-type PC methods based on Gauss-Legendre collocation points for nonstiff IVPs ⋮ RKN-type parallel block PC methods with Lagrange-type predictors ⋮ Parallel-iterated pseudo two-step Runge-Kutta-Nyström methods for nonstiff second-order IVPs
Cites Work
- A theory for Nyström methods
- Klassische Runge-Kutta-Nyström-Formeln mit SchrittweitenKontrolle für Differentialgleichungen \(\ddot x= f(t,x)\)
- Eine RKT-Formel für Differentialgleichungen der Form?? =f(t, x)
- A One-step Method of Order 10 for y″ = f(x, y)
- Eine Runge-Kutta-Nyström-Formel 9-ter Ordnung mit Schrittweitenkontrolle für Differentialgleichungenx =f(t, x)
- New Runge-Kutta algorithms for numerical simulation in dynamical astronomy
- Comparing Numerical Methods for Ordinary Differential Equations
- [https://portal.mardi4nfdi.de/wiki/Publication:5678377 A Runge-Kutta Nystr�m algorithm]
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