Paper Info
Title
An improved approximate Newton method for implicit Runge-Kutta formulas.
Abstract
Implicit Runge–Kutta (IRK) methods (such as the s-stage Radau IIA method with s=3,5, or 7) for solving stiff ordinary differential equation systems have excellent stability properties and high solution accuracy orders, but their high computing costs in solving their nonlinear stage equations have seriously limited their applications to large scale problems. To reduce such a cost, several approximate Newton algorithms were developed, including a commonly used one called the simplified Newton method. In this paper, a new approximate Jacobian matrix and two new test rules for controlling the updating of approximate Jacobian matrices are proposed, yielding an improved approximate Newton method. Theoretical and numerical analysis show that the improved approximate Newton method can significantly improve the convergence and performance of the simplified Newton method.
Year
DOI
Venue
2011
10.1016/j.cam.2011.05.027
Journal of Computational and Applied Mathematics
Keywords
Field
DocType
65L06,65H10
Runge–Kutta methods,Mathematical optimization,Quasi-Newton method,Ordinary differential equation,Jacobian matrix and determinant,Mathematical analysis,Numerical analysis,Mathematics,Secant method,Steffensen's method,Newton's method
Journal
Volume
Issue
ISSN
235
17
0377-0427
Citations 
PageRank 
References 
0
0.34
3
Authors
1
Name
Order
Citations
PageRank
Dexuan Xie16710.92