An error embedded method based on generalized Chebyshev polynomials

DOI10.1016/j.jcp.2015.11.021zbMath1352.65177OpenAlexW2204083381MaRDI QIDQ729313

WonKyu Jung, Junghan Kim, Sunyoung Bu, Phil Su Kim

Publication date: 20 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2015.11.021

zbMATH Keywords

collocation methodRunge-Kutta methodstiff initial value problemerror embedded methodgeneralized Chebyshev polynomial

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for stiff equations (65L04)

Related Items (3)

An embedded formula of the Chebyshev collocation method for stiff problems ⋮ A new one-step method with three intermediate points in a variable step-size mode for stiff differential systems ⋮ Unnamed Item

Uses Software

• Matlab
• MEBDF
• RODAS
• ode23
• ode45
• Ode15s
• ode113
• ode23s
• MATLAB ODE suite

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Analysis of adaptive mesh refinement for IMEX discontinuous Galerkin solutions of the compressible Euler equations with application to atmospheric simulations
• Nonlinear Fourier analysis for discontinuous conductivities: computational results
• Convergence on error correction methods for solving initial value problems
• Speeding up Newton-type iterations for stiff problems
• Some schemes for the implementation of implicit Runge-Kutta methods
• Stable pseudoanalytical computation of electromagnetic fields from arbitrarily-oriented dipoles in cylindrically stratified media
• A new eighth-order A-stable method for solving differential systems arising in chemical reac\-tions
• A fourth-order Runge-Kutta method based on BDF-type Chebyshev approximations
• High-order multi-implicit spectral deferred correction methods for problems of reactive flow.
• Conservative multi-implicit spectral deferred correction methods for reacting gas dynamics.
• Blended implementation of block implicit methods for ODEs
• Accurate long-term integration of dynamical systems
• Legendre-Gauss-Radau collocation method for solving initial value problems of first order ordinary differential equations
• Accelerating the convergence of spectral deferred correction methods
• An Iteration Scheme for Implicit Runge—Kutta Methods
• Generalized Chebyshev Interpolation and Its Application to Automatic Quadrature
• An Error Corrected Euler Method for Solving Stiff Problems Based on Chebyshev Collocation
• The MATLAB ODE Suite
• Solving Ordinary Differential Equations I
• Error Estimates and Adaptive Time-Step Control for a Class of One-Step Methods for Stiff Ordinary Differential Equations
• On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
• Iterated defect correction for the efficient solution of stiff systems of ordinary differential equations
• An Algorithm Based on the FFT for a Generalized Chebyshev Interpolation
• A-BDF: A Generalization of the Backward Differentiation Formulae
• Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods
• An MEBDF code for stiff initial value problems
• Two trigonometric quadrature formulae for evaluating hypersingular integrals
• A Chebyshev Collocation Method for Stiff Initial Value Problems and Its Stability
• Simple ECEM Algorithms Using Function Values Only
• A family of A-stable Runge Kutta collocation methods of higher order for initial-value problems
• Chebyshev Collocation Methods for Ordinary Differential Equations
• Implicit Runge-Kutta Processes
• A Chebyshev quadrature rule for one sided finite part integrals
• Runge-Kutta methods: Some historical notes

This page was built for publication: An error embedded method based on generalized Chebyshev polynomials