Multistep variable methods for exact integration of perturbed stiff linear systems
نویسندگان
چکیده
منابع مشابه
The integration of stiff systems of ODEs using multistep methods
The second order Ordinary Differential Equation (ODE) system obtained after semidiscretizing the wavetype Partial Differential Equation (PDE) with the Finite Element Method (FEM), shows strong numerical stiffness. Although it can be integrated using Matlab ode-solvers, the function ode15s offered by Matlab for solving stiff ODE systems does not result very efficient as its resolution requires t...
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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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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...
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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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Stiff behavior occurs in a variety of ODE systems relevant in applications. The notion of stiffness is a phenomenological one, and a stability and error analysis of numerical methods has been based either on simple models or particular problem structures. In particular, stiff initial value problems in standard singular perturbation form are well understood. However, problems of this type exhibi...
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ژورنال
عنوان ژورنال: Journal of Numerical Mathematics
سال: 2016
ISSN: 1570-2820,1569-3953
DOI: 10.1515/jnma-2013-1001