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S-ROCK: Chebyshev Methods for Stiff Stochastic Differential Equations

SIAM Journal of Scientific Computing, 2008
We present and analyze a new class of numerical methods for the solution of stiff stochastic differential equations (SDEs). These methods, called S-ROCK (for stochastic orthogonal Runge–Kutta Chebyshev), are explicit and of strong order 1 and possess ...
Assyr Abdulle
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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.

Mathematics of Computation, 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 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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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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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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Numerical Methods for Stiff, Quadratic and Josephson Interferometer Differential Equations.

1980
Abstract : THE TWO-PARAMETER CLASS OF ALL A-contractive two-step second-order formulas was derived for arbitrary step ratios. Similarly, the one-parameter class of all A-constractive two-step second-order formulas was derived for arbitrary step ratios. A specific A-contractive formula was derived which minimizes a measure of the global truncation error.
F. Odeh, W. Liniger
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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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A block method for the numerical integration of stiff systems of ordinary differential equations

BIT, 1979
A new approach to the approximate numerical integration of stiff systems of first order ordinary differential equations is developed. In this approach several different formulae are applied in a well defined cyclic order to produce highly accurate integration schemes with infinite regions of absolute stability.
Bond, J. E., Cash, J. R.
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Singular Perturbation for Stiff Equations Using Numerical Methods

1985
The present paper explores the following question: can the number-crunching power of the computer be used not only for generating numerical solutions, but also for deriving alternative formulations for the given problems? In other words, can the traditional role of human theoreticians also be performed by digital computers?
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