An \(A\)-stable extended trapezoidal rule for the integration of ordinary differential equations

DOI10.1016/0898-1221(85)90106-3zbMath0607.65043OpenAlexW1985950237WikidataQ127753655 ScholiaQ127753655MaRDI QIDQ1085572

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1016/0898-1221(85)90106-3

zbMATH Keywords

convergence numerical examples stiff systems \(A\)-stability nonlinear Gauß-Seidel iteration single-step implicit-integration algorithm

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (21)

New L-stable method for numerical solutions of ordinary differential equations ⋮ A class of stabilized extended one-step methods for the numerical solution of ODEs ⋮ Multistride \(L\)-stable fourth-order methods for the numerical solution of ODEs ⋮ Extended a-stable two-step methods for the numerical solution of ordinary differential equations ⋮ Numerical methods based on extended one-step methods for solving optimal control problems ⋮ Extended double-stride \(L\)-stable methods for the numerical solution of ODEs ⋮ On the generation of mono-implicit Runge-Kutta-Nyström methods by mono-implicit Runge-Kutta methods ⋮ An L-stable extended two-step method for the integration of ordinary differential equations ⋮ A general theory of stabilized extended one-step methods for odes ⋮ An extended trapezoidal formula for the diffusion equation ⋮ Optimal extended one-step schemes of exponential type for stiff initial-value problems ⋮ A class of one-step time integration schemes for second-order hyperbolic differential equations ⋮ An extended trapezoidal formula for the diffusion equation in two space dimensions ⋮ Extended one-step methods for the numerical solution of ordinary differential equations ⋮ A two step method for the numerical integration of stiff differential equations ⋮ Stabilized cubic c¹-spline collocation method for solving first-order ordinary initial value problems ⋮ Extended one-step time-integration schemes for convection-diffusion equations ⋮ A variable-step variable-order algorithm for systems of stiff odes ⋮ Numerical solution of the generalized Burgers' equation via spectral/spline methods ⋮ Singly-implicit stabilized extended one-step methods for second-order initial-value problems with oscillating solutions ⋮ Modified backward differentiation methods of the Adams-type based on exponential interpolation

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