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Weights of the exponential fitting multistep algorithms for first-order ODEs. (English) Zbl 0991.65061

Summary: We describe a numerical method for the calculation of the weights of the linear multistep algorithms for solving first-order differential equations. The main novelties are that (i) we admit nonequidistant mesh points in the partition and (ii) the weights are determined on the basis of the exponential functions \(\exp(\lambda_i x)\), \(i= 1,2,3,\dots\) rather than on the power function set, as it is done for the classical weights. In this way the method allows computing not only the weights of the well-established algorithms but also those of new ones. Another novelty consists in the construction of a general scheme for the error analysis of this kind of algorithms. Some relevant numerical illustrations are given.

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L70 Error bounds for numerical methods for ordinary differential equations
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References:

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