Analysis of backward differentiation formula for nonlinear differential-algebraic equations with 2 delays
نویسنده
چکیده
This paper is concerned with the backward differential formula or BDF methods for a class of nonlinear 2-delay differential algebraic equations. We obtain two sufficient conditions under which the methods are stable and asymptotically stable. At last, examples show that our methods are true.
منابع مشابه
Backward Differentiation Approximations of Nonlinear Differential/Algebraic Systems
Finite difference approximations of dynamical systems modelled by nonlinear, semiexplicit, differential/algebraic equations are analyzed. Convergence for the backward differentiation method is proved for index two and index three problems when the numerical initial values obey certain constraints. The appropriate asymptotic convergence rates and the leading error terms are determined.
متن کاملApplication of the block backward differential formula for numerical solution of Volterra integro-differential equations
In this paper, we consider an implicit block backward differentiation formula (BBDF) for solving Volterra Integro-Differential Equations (VIDEs). The approach given in this paper leads to numerical methods for solving VIDEs which avoid the need for special starting procedures. Convergence order and linear stability properties of the methods are analyzed. Also, methods with extensive stability r...
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 کاملWaveform Relaxation Methods of Nonlinear Integral - Differential - Algebraic Equations
WAVEFORM RELAXATION METHODS OF NONLINEAR INTEGRAL-DIFFERENTIAL-ALGEBRAIC EQUATIONS ∗1) Yao-lin Jiang (Department of Mathematical Sciences, Xi’an Jiaotong University, Xi’an 710049, China) Abstract In this paper we consider continuous-time and discrete-time waveform relaxation methods for general nonlinear integral-differential-algebraic equations. For the continuous-time case we derive the conve...
متن کاملNumerical Implementation of BDF2 via Method of Lines for Time Dependent Nonlinear Burgers’ Equation
In this paper an efficient unconditionally stable numerical scheme is proposed for solving one dimensional quasi linear Burgers’ equation. The proposed scheme comprises of semi discretization via method of lines for the space variable and backward differentiation formula of order two (BDF2) for the time variable. The method of lines reduces the quasi linear partial differential equation in to n...
متن کامل