Extended one-step methods for solving delay-differential equations
نویسندگان
چکیده
We discuss extended one-step methods of order three for the numerical solution of delay-differential equations. A convergence theorem and the numerical studies regarding the convergence factor of these methods are given. Also, we investigate the stability properties of these methods. The results of the theoretical studies are illustrated by numerical examples.
منابع مشابه
A class of Extended one-step methods for solving delay differential equations
We derive a class of extended one-step methods of order m for solving delay-differential equations. This class includes methods of fourth and fifth order of accuracy. Also, the class of these methods depends on two free parameters. A convergence theorem and convergence factor of these methods are given. In addition, we investigate the stability properties of these methods. The results of the ar...
متن کاملExtended One-Step Schemes for Stiff and Non-Stiff Delay Differential Equations
The importance of delay differential equations (DDEs), in modelling mathematical biological, engineering and physical problems, has motivated searchers to provide efficient numerical methods for solving such important type of differential equations. Most of these types of differential models are stiff, and suitable numerical methods must be introduced to simulate the solutions. In this paper, w...
متن کاملEXTENDED PREDICTOR-CORRECTOR METHODS FOR SOLVING FUZZY DIFFERENTIAL EQUATIONS UNDER GENERALIZED DIFFERENTIABILITY
In this paper, the (m+1)-step Adams-Bashforth, Adams-Moulton, and Predictor-Correctormethods are used to solve rst-order linear fuzzy ordinary dierential equations. The conceptsof fuzzy interpolation and generalised strongly dierentiability are used, to obtaingeneral algorithms. Each of these algorithms has advantages over current methods. Moreover,for each algorithm a convergence formula can b...
متن کاملSolving the liner quadratic differential equations with constant coefficients using Taylor series with step size h
In this study we produced a new method for solving regular differential equations with step size h and Taylor series. This method analyzes a regular differential equation with initial values and step size h. this types of equations include quadratic and cubic homogenous equations with constant coeffcients and cubic and second-level equations.
متن کاملStability of two classes of improved backward Euler methods for stochastic delay differential equations of neutral type
This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...
متن کامل