Analysis and implementation of TR-BDF2
type: Item
instance of: scholarly article
title: Analysis and implementation of TR-BDF2
zbMATH Open document ID: 0859.65076
DOI: 10.1016/0168-9274(95)00115-8
author: M. E. Hosea
author: L. F. Shampine
published in: Applied Numerical Mathematics
publication date: 1996-07-07T00:00:00Z
review text: This paper deals with the successful and popular one-step method, TR-BDF2, for the solution of systems of ordinary differential equations arising in circuit and device simulation [see \textit{R. E. Bank}, \textit{W. M. Coughran jun.}, \textit{W. Fichtner}, \textit{E. H. Grosse}, \textit{D. J. Rose} and \textit{R. K. Smith}, Transient simulation of silicon devices and circuits, IEEE Trans. Comput.-Aided Design 4, 436-451 (1985)]. This method can be viewed as an embedded diagonally implicit Runge-Kutta pair of orders 2 and 3. A detailed inspection yields new results on stability, continuous extension, implementation and on improved local error estimates. Numerical examples show the effectiveness of the refined method.
reviewed by: Rudolf Scherer
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L70
zbMATH DE Number: 897528
zbMATH Keywords: numerical examples
zbMATH Keywords: one-step method, TR-BDF2
zbMATH Keywords: systems
zbMATH Keywords: embedded diagonally implicit Runge-Kutta pair
zbMATH Keywords: stability
zbMATH Keywords: continuous extension
zbMATH Keywords: error estimates
describes a project that uses: ode45
describes a project that uses: Ode15s
describes a project that uses: ode113
describes a project that uses: VODE
describes a project that uses: ode23
describes a project that uses: ode23s
describes a project that uses: Matlab
describes a project that uses: RODAS
describes a project that uses: MATLAB ODE suite
MaRDI profile type: Publication
full work available at URL: 0168-9274(95)00115-8
OpenAlex ID: W2113101487
cites work: Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
cites work: An adaptive theta method for the solution of stiff and nonstiff differential equations
cites work: VODE: A Variable-Coefficient ODE Solver
cites work: A composite integration scheme for the numerical solution of systems of ordinary differential equations
cites work: A composite integration scheme for the numerical solution of systems of parabolic PDEs in one space dimension
cites work: The design of a variable-step integrator for the simulation of gas transmission networks
cites work: Comparing numerical methods for stiff systems of O.D.E:s
cites work: Q4000061
cites work: A New Recurrence for Computing Runge–Kutta Truncation Error Coefficients
cites work: Displacement or Residual Test in the Application of Implicit Methods for Stiff Problems
cites work: Local error control in SDIRK-methods
cites work: On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
cites work: SomeL-stable methods for stiff differential equations
cites work: Implementation of Implicit Formulas for the Solution of ODE<scp>s</scp>
cites work: ODE solvers and the method of lines
cites work: Error estimators for stiff differential equations
cites work: The MATLAB ODE Suite
cites work: An Attempt to Avoid Exact Jacobian and Nonlinear Equations in the Numerical Solution of Stiff Differential Equations
cites work: An AN-stable Rosenbrock-type method for solving stiff differential equations
description: scientific article; zbMATH DE number 897528