منابع مشابه
Sequential second derivative general linear methods for stiff systems
Second derivative general linear methods (SGLMs) as an extension of general linear methods (GLMs) have been introduced to improve the stability and accuracy properties of GLMs. The coefficients of SGLMs are given by six matrices, instead of four matrices for GLMs, which are obtained by solving nonlinear systems of order and usually Runge--Kutta stability conditions. In this p...
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The paper deals with stiff systems of differential equations. To solve this sort of system numerically is a diffult task. In spite of the fact that we come across stiff systems quite often in the common practice, a very interesting and promissing numerical method of solving systems of ordinary differential equations (ODE) based on Taylor series has appeared. The question was how to harness the ...
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Two model problems for stii oscillatory systems are introduced. Both comprise a linear superposition of N 1 harmonic oscillators used as a forcing term for a scalar ODE. In the rst case the initial conditions are chosen so that the forcing term approximates a delta function as N ! 1 and in the second case so that it approximates white noise. In both cases the fastest natural frequency of the os...
متن کاملThird Derivative Multistep Methods for Stiff Systems
Abstract: In this paper, we present a class of multistep methods for the numerical solution of stiff ordinary differential equations. In these methods the first, second and third derivatives of the solution are used to improve the accuracy and absolute stability regions of the methods. The constructed methods are A-stable up to order 6 and A(α)-stable up to order 8 so that, as it is shown in th...
متن کاملBalanced Implicit Methods for Stiff Stochastic Systems
This paper introduces some implicitness in stochastic terms of numerical methods for solving stiff stochastic differential equations and especially a class of fully implicit methods, the balanced methods. Their order of strong convergence is proved. Numerical experiments compare the stability properties of these schemes with explicit ones.
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2007
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.2855