A theory for Nyström methods
From MaRDI portal
Publication:1218253
DOI10.1007/BF01396335zbMath0307.65053MaRDI QIDQ1218253
Publication date: 1976
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/132389
Related Items (67)
Low order practical Runge-Kutta-Nyström methods ⋮ Solving directly special fourth-order ordinary differential equations using Runge-Kutta type method ⋮ Interpolants for Runge-Kutta-Nyström methods ⋮ Functionally-fitted block methods for second order ordinary differential equations ⋮ An optimized two-step hybrid block method for solving general second order initial-value problems ⋮ A note on a diagonally implicit Runge-Kutta-Nyström method ⋮ Perturbed collocation and symplectic RKN methods ⋮ Nyström methods and singular second-order differential equations ⋮ A simplified Nyström-tree theory for extended Runge-Kutta-Nyström integrators solving multi-frequency oscillatory systems ⋮ Multi-step hybrid methods for special second-order differential equations \(y^{\prime \prime}(t)=f(t,y(t))\) ⋮ A generalized Numerov method for linear second-order differential equations involving a first derivative term ⋮ Gauss-Runge-Kutta-Nyström methods ⋮ A feasible and effective technique in constructing ERKN methods for multi-frequency multidimensional oscillators in scientific computation ⋮ Solving second order initial value problems by a hybrid multistep method without predictors ⋮ Economical handling of Runge-Kutta-Nyström step rejection ⋮ Families of fifth order Nyström methods for y=f(x,y) and intervals of periodicity ⋮ Block third derivative method based on trigonometric polynomials for periodic initial-value problems ⋮ A phase- and amplification-fitted 5(4) diagonally implicit Runge-Kutta-Nyström pair for oscillatory systems ⋮ Trigonometrically fitted block Numerov type method for \(y = f(x, y, y')\) ⋮ An adaptive optimized Nyström method for second‐order IVPs ⋮ Grid-free weighted particle method applied to the Vlasov-Poisson equation ⋮ Order conditions for numerical methods for partitioned ordinary differential equations ⋮ A study of Rosenbrock-type methods of high order ⋮ Direct integrators of Runge-Kutta type for special third-order ordinary differential equations ⋮ Adaptive Nyström-Runge-Kutta-Methoden für gewöhnliche Differentialgleichungssysteme zweiter Ordnung ⋮ A continuous two-step method of order 8 with a block extension for \(y= f(x,y,y')\) ⋮ Order conditions for general linear Nyström methods ⋮ An alternative approach for order conditions of Runge-Kutta-Nyström methods ⋮ Symbolic derivation of Runge-Kutta-Nyström type order conditions and methods for solving \(y = f(x, y)\) ⋮ Modified ROW methods for stiff problems ⋮ On modifications of Runge-Kutta-Nyström methods for solving \(y^{(4)} = f(x, y)\) ⋮ General Nyström methods in Nordsieck form: error analysis ⋮ Implicit one-step block hybrid third-derivative method for the direct solution of initial value problems of second-order ordinary differential equations ⋮ A mono-implicit Runge-Kutta-Nyström modification of the Numerov method ⋮ A functionally-fitted block Numerov method for solving second-order initial-value problems with oscillatory solutions ⋮ High-order continuous third derivative formulas with block extensions fory″=f(x, y, y′) ⋮ A direct variable step block multistep method for solving general third-order ODEs ⋮ A four-stage implicit Runge-Kutta-Nyström method with variable coefficients for solving periodic initial value problems ⋮ Multi-step hybrid methods adapted to the numerical integration of oscillatory second-order systems ⋮ Order properties of symplectic Runge-Kutta-Nyström methods ⋮ A zero-dissipative Runge-Kutta-Nyström method with minimal phase-lag ⋮ Generalized Laguerre pseudospectral method based Laguerre interpolation ⋮ Méthodes de Nystrom pour l'équation différentielle y=f(x,y) ⋮ New \(4(3)\) pairs diagonally implicit Runge-Kutta-Nyström method for periodic IVPs ⋮ Unconditionally stable methods for second order differential equations ⋮ A class of continuous methods for general second order initial value problems in ordinary differential equations ⋮ A self-starting linear multistep method for a direct solution of the general second-order initial value problem ⋮ Legendre-Gauss collocation method for initial value problems of second order ordinary differential equations ⋮ Runge-Kutta methods for quadratic ordinary differential equations ⋮ Explicit integrator of Runge-Kutta type for direct solution of \(u^{(4)} = f(x, u, u', u)\) ⋮ Galerkin single-step methods for second-order hyperbolic equations ⋮ Recent advances in methods for numerical solution of O.D.E. initial value problems ⋮ Laguerre-Gauss collocation method for initial value problems of second order ODEs ⋮ Energy-preserving trigonometrically fitted continuous stage Runge-Kutta-Nyström methods for oscillatory Hamiltonian systems ⋮ The performance of the \(N\)-body integrator SSS ⋮ Superstable implicit Runge-Kutta methods for second order initial value problems ⋮ Symbolic derivation of Runge-Kutta-Nyström order conditions ⋮ Numerical methods for ordinary differential equations in the 20th century ⋮ An efficient optimized adaptive step-size hybrid block method for integrating \(w^{\prime \prime} = F (t, w, w^\prime)\) directly ⋮ Ein Runge-Kutta-Nyström-Formelpaar der ordnung 11(12) für Differentialgleichungen der Form \(y=f(x,y)\) ⋮ Conditions for the coefficients of Runge-Kutta methods for systems of n- th order differential equations ⋮ Ein Runge-Kutta-Nyström-Formelpaar der Ordnung 11(12) für Differentialgleichungen der Form \(y=f(x,y)\) ⋮ Regions of absolute stability of explicit Runge-Kutta-Nyström methods for \(y=f(x,y,y')\) ⋮ Absolute stability of explicit Runge-Kutta-Nyström methods for \(y=f(x,y,y')\) ⋮ New Runge-Kutta-Nyström formula-pairs of order 8(7), 9(8), 10(9) and 11(10) for differential equations of the form \(y=f(x,y)\) ⋮ On the numerical integration of second-order initial value problems with a periodic forcing function ⋮ Analysis of a class of multi-stage, multistep Runge-Kutta methods
Cites Work
This page was built for publication: A theory for Nyström methods