Third Derivative Multistep Methods for Stiff Systems
نویسندگان
چکیده
Abstract: In this paper, we present a class of multistep methods for the numerical solution of stiff ordinary differential equations. In these methods the first, second and third derivatives of the solution are used to improve the accuracy and absolute stability regions of the methods. The constructed methods are A-stable up to order 6 and A(α)-stable up to order 8 so that, as it is shown in the numerical experiments, they are superior for stiff systems.
منابع مشابه
On second derivative 3-stage Hermite--Birkhoff--Obrechkoff methods for stiff ODEs: A-stable up to order 10 with variable stepsize
Variable-step (VS) second derivative $k$-step $3$-stage Hermite--Birkhoff--Obrechkoff (HBO) methods of order $p=(k+3)$, denoted by HBO$(p)$ are constructed as a combination of linear $k$-step methods of order $(p-2)$ and a second derivative two-step diagonally implicit $3$-stage Hermite--Birkhoff method of order 5 (DIHB5) for solving stiff ordinary differential equations. The main reason for co...
متن کاملSequential second derivative general linear methods for stiff systems
Second derivative general linear methods (SGLMs) as an extension of general linear methods (GLMs) have been introduced to improve the stability and accuracy properties of GLMs. The coefficients of SGLMs are given by six matrices, instead of four matrices for GLMs, which are obtained by solving nonlinear systems of order and usually Runge--Kutta stability conditions. In this p...
متن کاملAn efficient computational algorithm for solving the nonlinear Lane-Emden type equations
In this paper we propose a class of second derivative multistep methods for solving some well-known classes of LaneEmden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. These methods, which have good stability and accuracy properties, are useful in deal with stiff ODEs. We show superiority of these methods by applying them on the some famous Lane-...
متن کاملPolynomial Formulation of Second Derivative Multistep Methods
Following the work of Enright [3] there has been interest in studying second derivative methods for solving stiff ordinary differential equations. Successful implementations of second derivative methods have been reported by Enright [3], Sacks-Davis [9], [10] and Addison[l]. Wallace and Gupta [13] have suggested a polynomial formulation of the usual first-derivative multistep methods. Recently ...
متن کاملSymplectic and symmetric methods for the numerical solution of some mathematical models of celestial objects
In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012