Analysis of a Chebyshev-based backward differentiation formulae and relation with Runge–Kutta collocation methods
DOI10.1080/00207161003631877zbMath1229.65115OpenAlexW1993016870MaRDI QIDQ5391509
Higinio Ramos, Raquel García Rubio
Publication date: 6 April 2011
Published in: International Journal of Computer Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/00207161003631877
stabilitynumerical exampleserror boundsstiff equationsinitial-value problemsbackward differentiation formula (BDF)Runge-Kutta collocation methodstruncated Chebyshev seriesBDF-type methodsChebyshev-Gauss-Lobatto nodes
Nonlinear ordinary differential equations and systems (34A34) Stochastic approximation (62L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical methods for stiff equations (65L04)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Stiffness of ODEs
- An improved class of generalized Runge-Kutta methods for stiff problems. II: The separated system case
- Exponential fitting BDF-Runge-Kutta algorithms
- A fourth-order Runge-Kutta method based on BDF-type Chebyshev approximations
- On the integration of stiff systems of O.D.E.s using extended backward differentiation formulae
- Solving ordinary differential equations by generalized Adams methods: Properties and implementation techniques
- On the potentiality of sequential and parallel codes based on extended trapezoidal rules (ETRs)
- A note on the efficient implementation of implicit methods for ODEs
- Dissipative Chebyshev exponential-fitted methods for numerical solution of second-order differential equations.
- Modification of the Richardson-Panovsky methods for precise integration of satellite orbits.
- Two low accuracy methods for stiff systems
- Boundary value methods based on Adams-type methods
- Stiff differential equations solved by Radau methods
- On the iterative solution of the algebraic equations in fully implicit Runge--Kutta methods
- On the relations between B\(_2\)VMs and Runge-Kutta collocation methods
- Exponential fitting BDF algorithms: explicit and implicit 0-stable methods
- On the numerical solution of stiff systems
- An Iteration Scheme for Implicit Runge—Kutta Methods
- Solving Ordinary Differential Equations I
- Analysis of the Enright-Kamel Partitioning Method for Stiff Ordinary Differential Equations
- VODE: A Variable-Coefficient ODE Solver
- A Fourth Order Exponentially Fitted Method
- A-BDF: A Generalization of the Backward Differentiation Formulae
- Barycentric Lagrange Interpolation
- Review Paper: Efficient numerical methods for the solution of stiff initial-value problems and differential algebraic equations
- Solving Ordinary Differential Equations II
- An almost L‐stable BDF‐type method for the numerical solution of stiff ODEs arising from the method of lines
- A family of A-stable Runge Kutta collocation methods of higher order for initial-value problems
- Efficient Integration Methods for Stiff Systems of Ordinary Differential Equations
- Multistep Methods with Variable Matrix Coefficients
- Integration of Stiff Equations
- General linear methods
This page was built for publication: Analysis of a Chebyshev-based backward differentiation formulae and relation with Runge–Kutta collocation methods
