Symbolic derivation of order conditions for hybrid Numerov-type methods solving \(y^{\prime\prime} =f(x,y)\)
type: Item
instance of: scholarly article
title: Symbolic derivation of order conditions for hybrid Numerov-type methods solving \(y^{\prime\prime} =f(x,y)\)
zbMATH Open document ID: 1143.65055
author: Ch. Tsitouras
author: I. Th. Famelis
published in: Journal of Computational and Applied Mathematics
publication date: 2008-07-11T00:00:00Z
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 34-04
Mathematics Subject Classification ID: 65Y15
zbMATH DE Number: 5300721
zbMATH Keywords: Numerov-type methods
zbMATH Keywords: order conditions
zbMATH Keywords: rooted trees
zbMATH Keywords: integer partitions
zbMATH Keywords: truncation error
zbMATH Keywords: MATHEMATICA\(^{\circledR}\)
describes a project that uses: Mathematica
describes a project that uses: Runge-Kutta Order Conditions
describes a project that uses: rktree
describes a project that uses: butcher
MaRDI profile type: Publication
full work available at URL: j.cam.2007.09.017
OpenAlex ID: W2091245503
cites work: Numerical treatment of O.D.Es.: The theory of A-methods
cites work: A one-step method for direct integration of structural dynamic equations
cites work: Implicit Runge-Kutta Processes
cites work: On Runge-Kutta processes of high order
cites work: Q4725642
cites work: Q4445112
cites work: A Matlab package for automatically generating Runge-Kutta trees, order conditions, and truncation error coefficients
cites work: A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems
cites work: Order conditions for a class of two-step methods for y'' = f (x, y)
cites work: Symbolic derivation of Runge-Kutta order conditions
cites work: Solving Ordinary Differential Equations I
cites work: A New Recurrence for Computing Runge–Kutta Truncation Error Coefficients
cites work: Q5581642
cites work: Canonical methods for Hamiltonian systems: Numerical experiments
cites work: High Phase-Lag-Order Runge--Kutta and Nyström Pairs
cites work: A General Family of Explicit Runge–Kutta Pairs of Orders $6(5)$
cites work: Q3243274
cites work: Symbolic derivation of Runge-Kutta methods
cites work: Explicit Numerov type methods with reduced number of stages.
cites work: Optimized explicit Runge-Kutta pair of orders \(9(8)\)
cites work: Stage reduction on P-stable Numerov type methods of eighth order
cites work: EXPLICIT EIGHTH ORDER TWO-STEP METHODS WITH NINE STAGES FOR INTEGRATING OSCILLATORY PROBLEMS
cites work: Cheap Error Estimation for Runge--Kutta Methods
DOI: 10.1016/J.CAM.2007.09.017
description: scientific article; zbMATH DE number 5300721