Results 151 to 160 of about 1,700 (198)
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Polynomial Chaos Expansions for Stiff Random ODEs
SIAM Journal of Scientific Computing, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wenjie Shi, Daniel M Tartakovsky
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A variable-step variable-order algorithm for systems of stiff odes [PDF]
International Journal of Computer Mathematics, 1997 A variable-step variable-order algorithm for stiff ODEs based on previously derived stabilized extended one-step methods is established. The developed code is tested on certain initial-value problems for systems of ODEs contained in the test set proposed
T Van Hecke, M Van Daele, H De Meyer
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BIT, 1993
This article investigates the performance of (explicit) one-step methods applied to stiff linear differential equations. The effects of ``freezing'' the coefficients and of diagonalizing the matrix is studied. By a series of interesting numerical experiments, it is shown that the scalar test equation \(y' = \lambda y\) does not correctly explain the ...
Higham, D.J., Trefethen, L.N.
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This article investigates the performance of (explicit) one-step methods applied to stiff linear differential equations. The effects of ``freezing'' the coefficients and of diagonalizing the matrix is studied. By a series of interesting numerical experiments, it is shown that the scalar test equation \(y' = \lambda y\) does not correctly explain the ...
Higham, D.J., Trefethen, L.N.
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SDIRK methods for stiff ODEs with oscillating solutions [PDF]
Journal of Computational and Applied Mathematics, 1997 New SDIRK methods specially adapted to the numerical solution of stiff systems of ODEs which are assumed to possess oscillating solutions are obtained. Our interest is centered on the dispersion (phase errors) and the dissipation (numerical damping), of ...
J M Franco, I Gomez, L Randez
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Matrix-Free Methods for Stiff Systems of ODE’s
SIAM Journal on Numerical Analysis, 1986The popular backward differentiation methods for solving stiff systems of ordinary differential equations, being implicit, require the solution of a linear algebraic system at each time step. The coefficient matrix is closely related to the Jacobian matrix of the differential system, and large systems may require considerable storage for the Jacobian ...
Brown, Peter N., Hindmarsh, Alan C.
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Stability and convergence at the PDE/stiff ode interface
Applied Numerical Mathematics, 1989Many numerical schemes for evolutionary partial differential equations can be viewed as method of lines schemes. The authors' main purpose is to show the theory of stiff ordinary differential equations (ODEs) to the field of analysis of numerical methods in partial differential equations.
Sanz-Serna, J. M., Verwer, J. G.
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A stiff ODE solver for an attached processor
Computer Physics Communications, 1982Abstract We present an implementation of a stiff ODE solver on the AP120B, and discuss design considerations which should be generally applicable to ODE software on attached processors of this type.
J.D. Pryce, J.W. Paine
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Computational experiments with algorithms for stiff ODEs
Computing, 1987The numerical performance of computer codes available to solve stiff systems of ODEs is evaluated. Three widely used codes of Gear/Hindmarsh, Gottwald/Wanner and Deuflhard/Bader are tested by numerous randomly generated examples which permit an arbitrary choice of the position and the number of the eigenvalues of the Jacobian.
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Methods for parallel integration of stiff systems of odes
BIT, 1992Parallelization of implicit Euler-type integration methods for stiff ordinary differential equations (ODEs) is obtained by decoupling the system into \(p\) subsystems for \(p\) processors. ``Internal'' solution components in each subsystem are treated implicitly, ``external'' solution components are extrapolated. The paper deals with the theory of this
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Description and Evaluation of a Stiff ODE Code DSTIFF
SIAM Journal on Scientific and Statistical Computing, 1985Summary: The paper describes and evaluates DSTIFF, a set of subroutines for solving stiff ordinary differential equations. The code is somewhat similar to the well-known packages LSODE, GEAR and DIFSUB but the present set of subroutines are based on least squares multistep formulas rather than the BDF. The paper describes the formulas used in the code,
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