Exponential fitting BDF algorithms and their properties

DOI10.1016/j.amc.2007.01.008zbMath1126.65060OpenAlexW2083763086MaRDI QIDQ2383736

Jesús Martín-Vaquero, Jesus Vigo Aguiar

Publication date: 19 September 2007

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

Full work available at URL: https://doi.org/10.1016/j.amc.2007.01.008

zbMATH Keywords

numerical examplesstiff systemsstability regionexponential fittinglocal truncation errorbackward differentiation formula (BDF) methodssystem of ODEmulti step finite difference method

Mathematics Subject Classification ID

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) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (13)

Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70th birthday ⋮ An adapted explicit hybrid four-step method for the numerical solution of perturbed oscillators ⋮ New optimized explicit modified RKN methods for the numerical solution of the Schrödinger equation ⋮ Fractional exponential fitting backward differential formulas for solving differential equations of fractional order ⋮ New optimized two-derivative Runge-Kutta type methods for solving the radial Schrödinger equation ⋮ A new embedded 5(3) pair of modified Runge-Kutta-Nyström methods for the numerical solution of the Schrödinger equation ⋮ A two-step method with vanished phase-lag and its first two derivatives for the numerical solution of the Schrödinger equation ⋮ Exponential fitted Gauss, Radau and Lobatto methods of low order ⋮ Exponentially fitted TDRK pairs for the Schrödinger equation ⋮ Exponential fitting BDF-Runge-Kutta algorithms ⋮ On the numerical solution of the heat conduction equations subject to nonlocal conditions ⋮ High order closed Newton-Cotes exponentially and trigonometrically fitted formulae as multilayer symplectic integrators and their application to the radial Schrödinger equation ⋮ An explicit trigonometrically fitted Runge–Kutta method for stiff and oscillatory problems with two frequencies

Uses Software

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

Cites Work

• Krylov methods for the incompressible Navier-Stokes equations
• Frequency evaluation in exponential fitting multistep algorithms for ODEs
• On the stability of exponential fitting BDF algorithms
• Stiffness in numerical initial-value problems
• Adapted BDF algorithms: Higher-order methods and their stability
• Exponential fitting BDF algorithms: explicit and implicit 0-stable methods
• Frequency evaluation for exponentially fitted Runge-Kutta methods
• On the numerical solution of stiff systems
• The MATLAB ODE Suite
• Adapted BDF algorithms applied to parabolic problems
• Diagonally Implicit Runge-Kutta Formulae with Error Estimates
• On Taylor Series and Stiff Equations
• An Efficient Numerical Method for Highly Oscillatory Ordinary Differential Equations
• On the Exponential Fitting of Composite, Multiderivative Linear Multistep Methods
• Efficient Solution of Parabolic Equations by Krylov Approximation Methods
• Comparing numerical methods for stiff systems of O.D.E:s
• A Fourth Order Exponentially Fitted Method
• Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
• Nineteen Dubious Ways to Compute the Exponential of a Matrix
• A General Procedure For the Adaptation of Multistep Algorithms to the Integration of Oscillatory Problems
• Expokit
• An MEBDF code for stiff initial value problems
• Exponential Integrators for Large Systems of Differential Equations
• P-stability and exponential-fitting methods for y = f(x,y)
• Efficient Integration Methods for Stiff Systems of Ordinary Differential Equations
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