منابع مشابه
Parallel Iteration of the Extended Backward Differentiation Formulas
The extended backward differentiation formulas (EBDFs) and their modified form (MEBDF) were proposed by Cash in the 1980s for solving initial-value problems (IVPs) for stiff systems of ordinary differential equations (ODEs). In a recent performance evaluation of various IVP solvers, including a variable-step-variable-order implementation of the MEBDF method by Cash, it turned out that the MEBDF...
متن کاملA model for stability of the semi-implicit backward differentiation formulas
A model is presented for stability for an extension of linear multistep methods for stiff ordinary differential equations. The method is based on a prediction followed by a fixed number of corrections obtained by a Newton scheme with inexact Jacobian matrix. The impact on stability of error in the matrix over a broad range of linear, constant coefficient equations is modeled. The model provides...
متن کاملParameter Range Reduction for ODE Models Using Cumulative Backward Differentiation Formulas
We consider fitting an ODE model to time series data of the system variables. We assume that the parameters of the model have some initial range of possible values and the goal is to reduce these ranges to produce a smaller parameter region from which to start a global nonlinear optimization algorithm. We introduce the class of cumulative backward differentiation formulas (CBDFs) and show that ...
متن کاملNumerical Solution of Nonlinear Differential Equations with Algebraic Constraints I: Convergence Results for Backward Differentiation Formulas
In this paper we investigate the behavior of numerical ODE methods for the solution of systems of differential equations coupled with algebraic constraints. Systems of this form arise frequently in the modelling of problems from physics and engineering; we study some particular examples from electrical networks, fluid dynamics and constrained mechanical systems. We show that backward differenti...
متن کاملDiagonally Implicit Block Backward Differentiation Formulas for Solving Ordinary Differential Equations
This paper focuses on the derivation of diagonally implicit two-point block backward differentiation formulas DI2BBDF for solving first-order initial value problem IVP with two fixed points. The method approximates the solution at two points simultaneously. The implementation and the stability of the proposed method are also discussed. A performance of the DI2BBDF is compared with the existing ...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2007
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.3162