Results 171 to 180 of about 2,092,411 (198)

Variable stepsize in Cowell's method

BIT, 1989
The author proposes a formula which is intended to facilitate fourth order piecewise constant step size implementation of Cowell's method.
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Supplement to Construction of Variable-Stepsize Multistep Formulas

Mathematics of Computation, 1986
Supplement to the author's paper in ibid. 47, 503-510 (1986; reviewed above).
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Reversible Long-Term Integration with Variable Stepsizes

SIAM Journal on Scientific Computing, 1997
The problem \(y'=f(y)\), \(y(0)=y_0\) is called \(\rho\)-reversible \((\rho\) is an invertible linear transformation in the phase space) if for all \(y\) the equation \(f(\rho y)= -\rho f(y)\) holds. Some Hamiltonian systems belong to this category.
Hairer, Ernst, Stoffer, Daniel
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On the Stability of Interpolatory Variable-Stepsize Adams Methods in Nordsieck Form

SIAM Journal on Numerical Analysis, 1989
In the existing ODE codes stepsize controls are incorporated. In order to ensure the stability of the integration process restrictions on the stepsize variation must be imposed. The authors consider various strategies for the stepsize selection and corresponding conditions for the allowable ratio \(h_{j+1}/h_ j\) of consecutive stepsize for the Adams ...
Calvo, M., Lisbona, F., Montijano, J.
exaly   +2 more sources

Variable-stepsize Runge–Kutta methods for stochastic Schrödinger equations

Physics Letters A, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wilkie, Joshua, Çetinbaş, Murat
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Advance in the theory of variable stepsize variable formula methods for ordinary differential equations

Proceedings of the conference on Numerical ordinary differential equations, 1989
A theory for the numerical solution of ordinary differential equations with variable stepsize, variable formula methods is given and applied in the selection of methods for solving large systems of ODE's arising in air pollution models.
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Variable Stepsizes in Symmetric Linear Multistep Methods

2001
It is well known the great deal of advantages of integrating reversible systems with symmetric methods. The correct qualitative behaviour is imitated, which leads also to quantitative advantageous properties with respect to the errors and their growth with time.
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Variable stepsize variable formula methods based on predictor-corrector schemes

Applied Numerical Mathematics, 1985
The use of fairly general predictor-corrector (PC) schemes of linear multistep (LM) formulae in the numerical solution of systems of ODE's is considered. It is assumed that both the stepsize and the PC scheme can be varied during the computational process.
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On The Stability of Variable Stepsize Adams Methods in Nordsieck Form

1987
The aim of our paper is to show that the stability of Adams methods can be ascertained under weaker assumptions than the ones given in [5] and [13]. In particular it is proved that (k+1)-value Adams methods remain stable if there exists a fixed p ≥ 0, so that after consecutive arbitrary stepsizes whose number is ≤p, there are at least k-1 steps of ...
Manuel Calvo, Francisco J. Lisbona, Juan I. Montijano   +2 more
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Numerical methods for SDEs - with variable stepsize implementation [PDF]

Efficient numerical solution of stochastic differential equations (SDEs) is important for applications in many fields. One possible way to reduce computational cost is by implementing adaptive stepsize schemes. Fixed stepsize implementations have limitations particularly when the SDEs are stiff as this forces the stepsize to be very small.
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