Hybrid BDF methods for the numerical solutions of ordinary differential equations

被引：16

作者：

Ebadi, Moosa ^{[1
]}

Gokhale, M. Y. ^{[2
]}

机构：

[1] Univ Pune, Dept Math, Pune, Maharashtra, India

[2] MIT Coll, Dept Math, Pune, Maharashtra, India

来源：

NUMERICAL ALGORITHMS | 2010年 / 55卷 / 01期

关键词：

Enright methods; MEBDF; Off-step point; General multistep methods; General linear methods; Multistep Runge-Kutta methods; A-stability; Nsoli; Fsolve; INITIAL-VALUE PROBLEMS; STIFF SYSTEMS; ODES; INTEGRATION;

D O I：

10.1007/s11075-009-9354-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we have presented the details of hybrid methods which are based on backward differentiation formula (BDF) for the numerical solutions of ordinary differential equations (ODEs). In these hybrid BDF, one additional stage point (or off-step point) has been used in the first derivative of the solution to improve the absolute stability regions. Stability domains of our presented methods have been obtained showing that all these new methods, we say HBDF, of order p, p = 2,4,..., 12, are A(alpha)-stable whereas they have wide stability regions comparing with those of some known methods like BDF, extended BDF (EBDF), modified EBDF (MEBDF), adaptive EBDF (A-EBDF), and second derivtive Enright methods. Numerical results are also given for five test problems.

引用

页码：1 / 17

页数：17

共 25 条

[1] DIAGONALLY IMPLICIT RUNGE-KUTTA METHODS FOR STIFF ODES [J].