Explicit, high-order Runge-Kutta-Nyström methods for parallel computers
From MaRDI portal
Publication:1308578
DOI10.1016/0168-9274(93)90145-HzbMath0787.65055MaRDI QIDQ1308578
Publication date: 24 May 1994
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
error controliteration schemeparallel computerexplicit Runge-Kutta-Nyström methodsvariable-step mode
Nonlinear ordinary differential equations and systems (34A34) Parallel numerical computation (65Y05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)
Related Items
Note on the performance of direct and indirect Runge-Kutta-Nyström methods, Functionally-fitted block methods for second order ordinary differential equations, Continuous parallel-iterated RKN-type PC methods for nonstiff IVPs, Block hybrid method using trigonometric basis for initial value problems with oscillating solutions, A trigonometrically fitted block method for solving oscillatory second-order initial value problems and Hamiltonian systems, Explicit symmetric Runge-Kutta-Nyström methods for parallel computers, Are Gauss-Legendre methods useful in molecular dynamics?, Unnamed Item, Solving second order initial value problems by a hybrid multistep method without predictors, Block third derivative method based on trigonometric polynomials for periodic initial-value problems, Trigonometrically fitted block Numerov type method for \(y = f(x, y, y')\), A family of explicit parallel Runge-Kutta-Nyström methods, Unnamed Item, A general class of explicit pseudo--two-step RKN methods on parallel computers, A continuous two-step method of order 8 with a block extension for \(y= f(x,y,y')\), An algorithm for second order initial and boundary value problems with an automatic error estimate based on a third derivative method, On a family of trigonometrically fitted extended backward differentiation formulas for stiff and oscillatory initial value problems, Parallel step-by-step methods, Fast convergence pirkn-type pc methods with adams-type predictors∗, High-order continuous third derivative formulas with block extensions fory″=f(x, y, y′), Twostep-by-twostep continuous PIRKN-type PC methods for nonstiff IVPs, Explicit pseudo two-step RKN methods with stepsize control, Some procedures for the construction of high-order exponentially fitted Runge-Kutta-Nyström methods of explicit type, Trigonometric symmetric boundary value method for oscillating solutions including the sine-Gordon and Poisson equations, Implicit third derivative Runge-Kutta-Nyström method with trigonometric coefficients, Explicit parallel two-step Runge-Kutta-Nyström methods, Parallel block pc methods with rkn-type correctors and adams-type predictors∗, Third derivative modification of \(k\)-step block Falkner methods for the numerical solution of second order initial-value problems, Embedded implicit Runge–Kutta Nyström method for solving second-order differential equations, 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
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Stability of collocation-based Runge-Kutta-Nyström methods
- Ein Runge-Kutta-Nyström-Formelpaar der Ordnung 11(12) für Differentialgleichungen der Form \(y=f(x,y)\)
- New Runge-Kutta-Nyström formula-pairs of order 8(7), 9(8), 10(9) and 11(10) for differential equations of the form \(y=f(x,y)\)
- Méthodes de Nystrom pour l'équation différentielle y=f(x,y)
- Unconditionally stable methods for second order differential equations
- Parallel block predictor-corrector methods of Runge-Kutta type
- Parallel iteration of high-order Runge-Kutta methods with stepsize control
- Note on the performance of direct and indirect Runge-Kutta-Nyström methods
- Klassische Runge-Kutta-Nyström-Formeln mit SchrittweitenKontrolle für Differentialgleichungen \(\ddot x= f(t,x)\)
- Ein Runge-Kutta-Nyström-Formelpaar der Ordnung 10(11) für Differentialgleichungen der Formy′ =f(x, y)
- 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)
- Resolution of Runge-Kutta-Nystrom condition equations through eighthorder
- New Runge-Kutta algorithms for numerical simulation in dynamical astronomy
- Comparing Numerical Methods for Ordinary Differential Equations
- Implicit Runge-Kutta Processes