Implementing Second-Derivative Multistep Methods Using the Nordsieck Polynomial Representation
نویسندگان
چکیده
منابع مشابه
Polynomial 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 کاملextensions of some polynomial inequalities to the polar derivative
توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی
15 صفحه اولThird Derivative Multistep Methods for Stiff Systems
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 th...
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 کاملOn the polar derivative of a polynomial
For a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, Dewan et al [K. K. Dewan, N. Singh and A. Mir, Extension of some polynomial inequalities to the polar derivative, J. Math. Anal. Appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). In this paper we improve and extend the above inequality. Our result generalizes certai...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1978
ISSN: 0025-5718
DOI: 10.2307/2006255