Block predictor-corrector schemes for the parallel solution of ODEs

DOI10.1016/S0898-1221(97)00032-1zbMath0872.65069WikidataQ128109547 ScholiaQ128109547MaRDI QIDQ1356867

O. Diekmann

Publication date: 20 October 1997

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

stabilitycomputational complexityparallel computationerror boundpredictor-corrector methodsfourth-order block method

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) 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) Error bounds for numerical methods for ordinary differential equations (65L70) Complexity and performance of numerical algorithms (65Y20)

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Implicit \(r\)-point block backward differentiation formula for solving first-order stiff ODEs, Stein implicit Runge-Kutta methods with high stage order for large-scale ordinary differential equations, 3-point block backward differentiation formula with an off-step point for the solutions of stiff chemical reaction problems, A large parallel block predictor-corrector method for initial value problems, Derivation of new block methods for the numerical solution of first-order IVP's, A Fast Block Krylov Implicit Runge–Kutta Method for Solving Large-Scale Ordinary Differential Equations, Derivation of a new block method similar to the block trapezoidal rule for the numerical solution of first-order IVPs, A new variable step size block backward differentiation formula for solving stiff initial value problems

Cites Work

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• Invariants and numerical methods for ODEs
• Efficient block predictor-corrector methods with a small number of corrections
• Parallel Solution of ODE’<scp>s</scp> by Multiblock Methods
• Parallel Methods for the Numerical Solution of Ordinary Differential Equations
• Parallel Solution of Ordinary Differential Equations
• Block Implicit One-Step Methods
• A-stable block implicit one-step methods