Second Derivative Multistep Methods for Stiff Ordinary Differential Equations

Enright, W. H.

doi:10.1137/0711029

Cited by 225 publications

(169 citation statements)

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“…En la segunda mitad de la década de los 70, autores como Enright y Henrici, propusieron una serie de esquemas implícitos no lineales multipaso multiderivada de orden Q con tamaño de paso uniforme, con ciertas ventajas teóricas y prácticas para el tratamiento de sistemas de ecuaciones diferenciales ordinarias (ver [8] con continuidad en trabajos como [13]). Para este trabajo, se estudiaron los esquemas conocidos como "fórmulas de segundo orden" con el objetivo de validar una "familia" de métodos eficientes para el tratamiento de la rigidez.…”

Section: Estrategia Combinadaunclassified

Estimación del error en cierta clase de métodos numéricos combinados de estrategia recorrectora

Marrero

Baguer

2004

RMTA

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ResumenEl siguiente trabajo brinda un análisis del orden de los errores de aproximación y de redondeo que se cometen al combinar esquemas numéricos de estrategia recorrectora, de la familia Adams-Moulton-Bashfort. Estos métodos se utilizan en el tratamiento numérico del problema de estimación en modelos definidos por sistemas dinámicos de EDO.Nuestro propósito es disponer de una "familia o clase" de métodos que sean eficientes o al menos competitivos al abordar la resolución numérica de este tipo de problemas, Esta estrategia es compatible con las tendencias actuales que emplean modelos con funciones objetivos mínimo-cuadradas para el ajuste de curvas, que usan métodos de optimización sin y con restricciones, para resolver un problema discretizado por un esquema numérico que puede ser implícito, semi-implícito o explícito.Palabras clave: Métodos numéricos de estrategia recorrectora, multipasos, rigidez, errores de aproximación y redondeo. AbstractThis paper shows an analysis of the order for the approximation and roundoff errors in combined numerical scheme with recorrector strategy of Adams-MoultonBashfort family. These methods are used for the numerical solution of the estimation problem in models defined by dynamical ODE. Our interest is avail oneself of "family or kind" of methods which will be efficient or at least competitive for the numerical solutions of this type of problems. This strategy is consistent with the present tendency

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Section: Estrategia Combinadaunclassified

Estimación del error en cierta clase de métodos numéricos combinados de estrategia recorrectora

Marrero

Baguer

2004

RMTA

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“…For the sake of comparison, in Appendix A we include the details of the truncation error and stability of the stiff formulae used by Gear. Table 3 Details of Chebyshev approximation formulae CHEB2 and CHEB4 Table 4 Coefficients of formulae FMPD50 Modifier polynomial C(x) = V¡L0c¡xl, c1 = -1.0 Also, at the suggestion of the referee, we present in Appendix B the coefficients of the conventional representation of the formulae CHEBl, CHEB2, CHEB3, CHEB4, Kutta formulae, a variable-order method based on the second derivative multistep formulae developed by Enright (1974) and a fourth-order method based on the trapezoidal rule with extrapolation developed by Lindberg (1971). The main conclusion of this study is that generally the methods based on Runge-Kutta formulae are unreliable (except for solving linear problems).…”

Section: Figurementioning

confidence: 99%

Some New High-Order Multistep Formulae for Solving Stiff Equations

Gupta¹

1976

Mathematics of Computation

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“…(3.7)]. In addition, the present paper explores the relationship between the blended formulas of Skeel and Kong [12] and the second derivative methods of Enright [3] when Nordsieck representation is used. We also discuss some advantages of the polynomial formulation.…”

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confidence: 99%

“…Enright [4] presents another set of second derivative formulas which are stiffly stable up to order 7. The first set of Enright's formulas has been implemented by Enright [3], Sacks-Davis [9], [10], and Addison [1].…”

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confidence: 99%