Modified extended backward differentiation formulae for the numerical solution of stiff initial value problems in ODEs and DAEs

Cash, J. R.

doi:10.1016/s0377-0427(00)00463-5

Cited by 91 publications

(58 citation statements)

References 14 publications

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“…Thus, the MEBDF formulae can be regarded as a third path, aside (i) linear multistep methods, which are cheap to implement but, due to the famous Dahlquist's barrier, at higher orders have pure stability, and (ii) implicit Runge-Kutta methods with potentially excellent stability but expensive implementation. The origins of the new approach were described by Cash [21].…”

Section: The Origins Of the Modified Extended Bdfmentioning

confidence: 99%

Application of the MEBDFV solver to dynamic simulation of some specific multibody systems: an example of a cervical spine model

Fritzkowski

Walczak

2014

Int. J. Dynam. Control

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Application of the MEBDFV code in multibody dynamics is discussed. The solver is based on the modified extended backward differentiation formulae of Cash. It is especially suited for the solution of differential-algebraic equations with time-and state-dependent mass matrix. Such a case can occur when motion of a multibody open-chain system is described within the classical Lagrangian formalism, which still has some advantages. An outline of the numerical algorithm is given. As an example, a simplified mathematical model of the human head-cervical spine system is presented. In a numerical experiment the model is used to analyze motion of the head-neck during rear-end impact which may lead to whiplash injury. The obtained results are compared to literature data. Performance of the MEBDFV solver is examined in terms of algorithmic energy conservation. The test is based on an appropriately formulated 'kinetic energy-work' relation.

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Section: The Origins Of the Modified Extended Bdfmentioning

confidence: 99%

Application of the MEBDFV solver to dynamic simulation of some specific multibody systems: an example of a cervical spine model

Fritzkowski

Walczak

2014

Int. J. Dynam. Control

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“…Cash proposed the Modified Extended BDF (MEBDF) method, which combines better stability properties and higher order of convergence than BDF, but requires more computations per step [33,34]. One timestep with the MEBDF method consists of three BDF steps and an evaluation step.…”

Section: T) By Expanding F(ẏ(t) X(t) T)mentioning

confidence: 99%

Modelling and Discretization of Circuit Problems

Günther

Feldmann

Maten

2005

Handbook of Numerical Analysis

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“…Uma dessas metodologias é o método BDF modificado e estendido (MEBDF), apresentando características particularmente eficientes durante o processo de solução de sistemas de EDAs com índice menor e igual a três (Cash, 2000).…”

Section: Método De Diferenciação Regressiva Modificado Estendidounclassified

“…Portanto, a metodologia é considerada A(α)-estável para ordens menores ou iguais a nove e Rígida-estável para ordens maiores que nove. Estas propriedades de estabilidade são consideravelmente melhores que as atingidas pelos métodos baseados nas fórmulas BDF convencionais (Cash, 1983;Cash e Considine, 1992;Cash, 2000).…”

Section: Método De Diferenciação Regressiva Modificado Estendidounclassified

“…Nota-se um crescente interesse pelo desenvolvimento/adaptação de metodologias numéricas apilcadas na solução de sistemas de EDAs (Ascher e Petzold, 1998;Brenan et al, 1996;Cash, 2000;Mazzia e Iavernaro, 2003;Petzold e LI, 2000). Este interesse tem produzido e disponibilizado novas alternativas de solução e o presente trabalho procura integrar e aproveitar adequadamente estes avanços com interesse específico em fenômenos de estabilidade em sistemas elétricos.…”

Section: Introductionunclassified

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Técnicas de solução de sistemas de equações diferenciais e algébricas: aplicação em sistemas de energia elétrica

Pessanha¹,

Portugal²,

Paz³

2005

Sba Controle & Automação

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The present work investigates and compares the computational performance of numerical techniques applied to the solution of algebraic and differential equations (DAEs) representing power systems and their components. Among the considered techniques, emphasis was given to the method known as Modified Extended Backward Differentiation Formulae (MEBDF), due to its numerical stability properties that conventional Backward Differentiation Formulae (BDF) methods do not have, and these properties may avoid numerical troubles during DAEs solution. The comparison is made through computational tests related to simulations of power system short-and long-term stability phenomena (transient angular stability and long-term voltage stability), using IEEE system-test. The main objective was to check the computational efficiency of these numerical techniques. The computational aspect is related to the simulation CPU time. técnicas numéricas aplicadas na solução de Equações Diferenciais e Algébricas (EDAs) representando sistemas elé-tricos e seus componentes. Entre os métodos considerados, destaca-se o método conhecido como Método de Diferenciação Regressiva Modificado Estendido (MEBDF), por este apresentar propriedades de estabilidade numérica que os Mé-todos de Diferenciação Regressiva (BDF) convencionais não apresentam, sendo que estas propriedades podem evitar problemas numéricos durante a solução das EDAs. As técni-cas são comparadas através de testes envolvendo simulações computacionais no domínio do tempo de fenômenos de estabilidade de curta-, e de longa-duração (angular e de tensão, respectivamente) em sistemas-teste do IEEE. O objetivo principal foi verificar a eficiência dessas técnicas numéri-cas sob o ponto de vista computacional, sem comprometer a precisão. O aspecto computacional está relacionado com o tempo de cpu gasto nas simulações.

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Modified extended backward differentiation formulae for the numerical solution of stiff initial value problems in ODEs and DAEs

Cited by 91 publications

References 14 publications

Application of the MEBDFV solver to dynamic simulation of some specific multibody systems: an example of a cervical spine model

Application of the MEBDFV solver to dynamic simulation of some specific multibody systems: an example of a cervical spine model

Modelling and Discretization of Circuit Problems

Técnicas de solução de sistemas de equações diferenciais e algébricas: aplicação em sistemas de energia elétrica

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