Doubly quasi-consistent parallel explicit peer methods with built-in global error estimation

DOI10.1016/j.cam.2009.10.020zbMath1206.65179OpenAlexW2018209799MaRDI QIDQ847188

G. Yu. Kulikov, Rüdiger Weiner

Publication date: 12 February 2010

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

Full work available at URL: https://doi.org/10.1016/j.cam.2009.10.020

zbMATH Keywords

superconvergenceembedded formulasdoubly quasi-consistent numerical schemes

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items

Two-step peer methods with equation-dependent coefficients, Doubly quasi-consistent fixed-stepsize numerical integration of stiff ordinary differential equations with implicit two-step peer methods, Two-step peer methods with continuous output, Variable-stepsize doubly quasi-consistent singly diagonally implicit two-step peer pairs for solving stiff ordinary differential equations, Efficient error control in numerical integration of ordinary differential equations and optimal interpolating variable-stepsize peer methods, Generalizing global error estimation for ordinary differential equations by using coupled time-stepping methods, Functionally fitted explicit two step peer methods, Exponentially fitted two-step peer methods for oscillatory problems, On the derivation of explicit two-step peer methods, Time-accurate and highly-stable explicit peer methods for stiff differential problems, Estimating the domain of absolute stability of a numerical scheme based on the method of solution continuation with respect to a parameter for solving stiff initial value problems, Nested implicit Runge-Kutta pairs of Gauss and Lobatto types with local and global error controls for stiff ordinary differential equations, Variable-stepsize doubly quasi-consistent parallel explicit peer methods with global error control, Local and global error estimation and control within explicit two-step peer triples, Adapted explicit two-step peer methods, A Singly Diagonally Implicit Two-Step Peer Triple with Global Error Control for Stiff Ordinary Differential Equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• One-leg variable-coefficient formulas for ordinary differential equations and local-global step size control
• Constant coefficient linear multistep methods with step density control
• On quasi-consistent integration by Nordsieck methods
• Thirteen ways to estimate global error
• Global error estimation and the backward differentiation formulas
• Numerical investigations on global error estimation for ordinary differential equations
• Superconvergent explicit two-step peer methods
• Explicit two-step peer methods
• Time-step selection algorithms: adaptivity, control, and signal processing
• Global error estimation and extrapolated multistep methods for index 1 differential-algebraic systems
• Solving Ordinary Differential Equations I
• On Global Error Estimation and Control for Initial Value Problems
• Global error control in implicit parallel peer methods
• On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
• Analysis of Fixed-Stepsize Methods
• Consistency of Nordsieck Methods
• Explicit, Time Reversible, Adaptive Step Size Control
• Local and global error estimation in Nordsieck methods