On the stability of exponential fitting BDF algorithms

Authors:
J. Vigo-Aguiar;J. Martín-Vaquero;R. Criado
Affiliations:
Facultad de Ciencias, Universidad de Salamanca, Salamanca, Spain and Department of Pure and Applied Mathematics, University of Salamanca, Salamanca 37008, Spain;ETS Ingenieros Industriales, Universidad de Salamanca, Bejar, Spain;ESCET, Universidad Rey Juan Carlos, Madrid, Spain
Venue:
Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
Year:
2005

Citing 3
Cited 5

Numerical methods for ordinary differential systems: the initial value problem

Numerical methods for ordinary differential systems: the initial value problem
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
A General Procedure For the Adaptation of Multistep Algorithms to the Integration of Oscillatory Problems

SIAM Journal on Numerical Analysis

Exponential fitting BDF algorithms: explicit and implicit 0-stable methods

Journal of Computational and Applied Mathematics - Special issue on computational and mathematical methods in science and engineering (CMMSE-2004)
Parameter range reduction for ODE models using cumulative backward differentiation formulas

Journal of Computational and Applied Mathematics
Explicit finite difference schemes adapted to advection-reaction equations

International Journal of Computer Mathematics - Recent Advances in Computational and Applied Mathematics in Science and Engineering
Smoothing schemes for reaction-diffusion systems with nonsmooth data

Journal of Computational and Applied Mathematics
On the numerical solution of the heat conduction equations subject to nonlocal conditions

Applied Numerical Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present BDF type formulas capable of the exact integration (with only round-off errors) of differential equations whose solutions are linear combinations of an exponential with parameter λ and ordinary polynomials. For λ = 0 new formulas reduces to the classical BDF formulas. Plots of their 0-stability regions in terms of λ are provided. Plots of their regions absolute stability that include all the negative real axis are provided. Numerical examples shows the efficiency of the proposed codes, specially when we are integrating stiff oscillatory problems.