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AN A-STABLE MODIFICATION OF ADAMS-BASHFORTH's METHOD FOR THE NUMERICAL INTEGRATION OF ORDINARY STIFF DIFFERENTIAL EQUATIONS

, 1969
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A two step method for the numerical integration of stiff differential equations

International Journal of Computer Mathematics, 2000
We examine a single-step implicit-integration algorithm which is obtained by a modification of the well-known Simpson rule. The accuracy and stability properties of these methods are investigated. The obtained new method is a fourth-order numerical process and preserves the property of A-stability of the Simpson rule. Numerical results for the solution
Hasan Bulut, Mustafa Inç
exaly   +3 more sources

Numerical approximation to semi-linear stiff neutral equations via implicit–explicit general linear methods

Mathematics and Computers in Simulation, 2022
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Chengjian Zhang
exaly   +2 more sources

Balanced Implicit Methods for Stiff Stochastic Systems

SIAM Journal on Numerical Analysis, 1998
This paper introduces some implicitness in stochastic terms of numerical methods for solving stiff stochastic differential equations and especially aclass of fully implicit methods, the balanced methods.
Eckhard Platen, G N Milstein
exaly   +2 more sources

Numerical methods for solving stiff systems of MHD-equations

Computational Mathematics and Modeling, 1991
A number of methods for numerical solving of the MHD equations are briefly discussed in the case of tokamak conditions. The considered plasma is toroidal, compressible, inviscid and has a constant electrical conductivity.
Paskonov, V. V., Shagirov, Eh. A.
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Numerical methods for stiff equations and singular perturbation problems

Mathematical Biosciences, 1983
1. Introduction.- Summary.- 1.1. Stiffness and Singular Perturbations.- 1.1.1. Motivation.- 1.1.2. Stiffness.- 1.1.3. Singular Perturbations.- 1.1.4. Applications.- 1.2. Review of the Classical Linear Multistep Theory.- 1.2.1. Motivation.- 1.2.2. The Initial Value Problem.- 1.2.3. Linear Multistep Operators.- 1.2.4.
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Numerical Methods for Stiff Ordinary and Elliptic Partial Differential Equations.

1985
Abstract : The research under this effort was concerned with stable high-order methods for nonlinear stiff systems of ordinary differential equations, relaxation methods for large scale circuit analysis, and fast direct methods for elliptic partial differential equations on general regions.
F. Odeh, L. Werner
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Numerical methods of boundary layer type for stiff systems of differential equations

Computing, 1973
Stiff systems of ordinary differential equations are difficult to deal with numerically. There is an equivalence between a subclass of stiff systems and differential equations subjected to singular perturbations. We use the characterization of the solution of this class of equations in terms of boundary layers as a means of generating numerical ...
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A Numerical Method to Integrate Stiff Systems of Ordinary Differential Equations

1980
Abstract : A method is described for the efficient integration of stiff systems of ordinary differential equations. The method, based on a predictor-corrector formulation, uses the Jacobian in a non-standard fashion. The resulting program is compared with EPISODE, a standard stiff integrator, for a number of systems of ordinary differential equations ...
M. D. Kregel, J. M. Heimerl, T. P. Coffee   +2 more
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Explicit multistep method for the numerical solution of stiff differential equations

Computational Mathematics and Mathematical Physics, 2007
An explicit multistep method of variable order for integrating stiff systems with high accuracy and low computational costs is examined. To stabilize the computational scheme, componentwise estimates are used for the eigenvalues of the Jacobian matrix having the greatest moduli. These estimates are obtained at preliminary stages of the integration step.
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