Advances in the theory of variable stepsize variable formula methods for ordinary differential equations

DOI10.1016/0096-3003(89)90120-3zbMath0674.65059OpenAlexW4254055109MaRDI QIDQ1121656

Zahari Zlatev

Publication date: 1989

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0096-3003(89)90120-3

zbMATH Keywords

air pollutionlarge systemsconsistentpredictor-corrector schemesconvergent methodsimplicit/explicit methodsvariable stepsize, variable formula methodszero stable

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Ecology (92D40) Numerical methods for initial value problems involving ordinary differential equations (65L05) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items

Running air pollution models on the connection machine, Efficient implementation of advanced Richardson extrapolation in an atmospheric chemical scheme

Uses Software

• DIFSUB
• ODEPACK

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stability of multistep-methods on variable grids
• On the zero-stability of the 3-step BDF-formula on nonuniform grids
• Stability restrictions on time-stepsize for numerical integration of first-order partial differential equations
• Mathematical model for studying the sulphur pollution over Europe
• Variable stepsize variable formula methods based on predictor-corrector schemes
• Implementation of a variable stepsize variable formula method in the time-integration part of a code for treatment of long-range transport of air pollutants
• Application of predictor-corrector schemes with several correctors in solving air pollution problems
• Parallel methods for ordinary differential equations
• Zero-stability properties of the three-ordinate variable stepsize variable formula methods
• Stability properties of variable stepsize variable formula methods
• Consistency and convergence of general linear multistep variable stepsize variable formula methods
• Numerical solution of ordinary differential equations
• Convergence and stability in the numerical integration of ordinary differential equations
• Jacobian Matrix Properties and Their Impact on Choice of Software for Stiff ODE Systems
• The Convergence of Variable-Stepsize, Variable-Formula, Multistep Methods
• The Stability of Variable-Stepsize Nordsieck Methods
• Quasilinear Multistep Methods and Variable Step Predictor–Corrector Methods for Neutral Functional-Differential Equations
• Two-parameter families of predictor-corrector methods for the solution of ordinary differential equations
• Automatic Solution of Differential Equations Based on the User of Linear Multistep Methods
• Runge-Kutta Starters for Multistep Methods
• Numerical Solution of Ordinary Differential Equations: Is There Anything Left to Do?
• The Effect of Variable Mesh Size on the Stability of Multistep Methods
• Stability and Convergence of Variable Order Multistep Methods
• The automatic integration of ordinary differential equations
• Corrigendum