B-convergence of the implicit midpoint rule and the trapezoidal rule
From MaRDI portal
Publication:1069677
DOI10.1007/BF01936143zbMath0584.65048OpenAlexW2063840785MaRDI QIDQ1069677
Publication date: 1985
Published in: BIT (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01936143
error boundsstiff problemsimplicit midpoint methodvariable stepsizessecond order optimal B-convergencetrapezoidal methods
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
Stability and B-convergence of linearly implicit Runge-Kutta methods, B-convergence properties of defect correction methods. I, II, Stability and Convergence of the Peaceman-Rachford ADI Method for Initial-Boundary Value Problems, The order of B-convergence of algebraically stable Runge-Kutta methods, On the maximum order of optimal B-convergence of Lobatto III C schemes, Implicit runge-kutta methods for differential inclusions, A study of B-convergence of linearly implicit Runge-Kutta methods, Characterization of B-convergent Runge-Kutta methods for strictly dissipative initial value problems, The dichotomy of stiffness: Pragmatism versus theory, Algebraic stability and error propagation in Runge-Kutta methods, B-convergence: A survey, B-convergence of general linear methods for stiff problems., The logarithmic norm. History and modern theory, Stability and B-convergence of general linear methods, On the relation between algebraic stability and B-convergence for Runge- Kutta methods, An efficient family of strongly A-stable Runge-Kutta collocation methods for stiff systems and DAEs. II: Convergence results, The implicit midpoint rule applied to discontinuous differential equations, Trapezoidal and midpoint splittings for initial-boundary value problems, A new approach to optimal B-convergence, Runge-Kutta methods: Some historical notes, Gauss-Runge-Kutta time discretization of wave equations on evolving surfaces, Fitted strong stability-preserving schemes for the Black-Scholes-Barenblatt equation, An algebraic characterization of B-convergent Runge-Kutta methods, Convergence of linear multistep and one-leg methods for stiff nonlinear initial value problems, Asymptotic error expansions for stiff equations: An analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case, The order of B-convergence of the Gaussian Runge-Kutta method, A study of B-convergence of Runge-Kutta methods, Arbitrary high order A-stable and B-convergent numerical methods for ODEs via deferred correction
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Asymptotic expansions of the global error for the implicit midpoint rule (stiff case)
- Error estimates over infinite intervals of some discretizations of evolution equations
- Algebraic stability and error propagation in Runge-Kutta methods
- Error estimates for Galerkin methods for quasilinear parabolic and elliptic differential equations in divergence form
- Stability of Two-Step Methods for Variable Integration Steps
- Stability Properties of Implicit Runge–Kutta Methods
- Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems
- Non-linear stability of a general class of differential equation methods
- The Concept of B-Convergence
- On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
- On error bounds forG-stable methods
- Contractive methods for stiff differential equations Part II
- A Note on Trapezoidal Methods for the Solution of Initial Value Problems
- A special stability problem for linear multistep methods