Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations

被引：31

作者：

Jackiewicz, Z ^{[1
]}

Tracogna, S ^{[1
]}

机构：

[1] ARIZONA STATE UNIV,DEPT MATH,TEMPE,AZ 85287

来源：

NUMERICAL ALGORITHMS | 1996年 / 12卷 / 3-4期

关键词：

continuous two-step Runge-Kutta method; convergence; order and stage order;

D O I：

10.1007/BF02142812

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A general class of variable stepsize continuous two-step Runge-Kutta methods is investigated. These methods depend on stage values at two consecutive steps. The general convergence and order criteria are derived and examples of methods of order p and stage order q=p or q=p-1 are given for p less than or equal to 5. Numerical examples are presented which demonstrate that high order and high stage order are preserved on nonuniform meshes with large variations in ratios between consecutive stepsizes.

引用

页码：347 / 368

页数：22

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