Two-step modified collocation methods with structured coefficient matrices

被引：23

作者：

D'Ambrosio, Raffaele ^{[1
]}

Paternoster, Beatrice ^{[1
]}

机构：

[1] Univ Salerno, Dipartimento Matemat, I-84084 Fisciano, Sa, Italy

来源：

APPLIED NUMERICAL MATHEMATICS | 2012年 / 62卷 / 10期

关键词：

Two-step Runge-Kutta methods; Almost collocation methods; A-stability; L-stability; Singly implicit Runge-Kutta methods; Diagonally implicit Runge-Kutta methods; ORDINARY DIFFERENTIAL-EQUATIONS; VOLTERRA INTEGRAL-EQUATIONS; GENERAL LINEAR METHODS; RUNGE-KUTTA METHODS;

D O I：

10.1016/j.apnum.2012.06.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the context of the numerical integration of initial value problems based on ordinary differential equations, it is the purpose of this paper to introduce a modification of two-step collocation methods, in order to obtain coefficient matrices with a structured shape, to get an efficient implementation. Our aim is the development of new collocation-based methods having high order of convergence and strong stability properties (e.g. A-stability and L-stability). We present the constructive technique, discuss the order of convergence and the stability properties of the resulting methods and provide some numerical results confirming the theoretical expectations. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：1325 / 1334

页数：10

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