Construction of high order diagonally implicit multistage integration methods for ordinary differential equations

Applied Numerical Mathematics

Volumn 27, Issue 1, 1998, Pages 1-12

  Butcher, J C ^a   Jackiewicz, Z ^b  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

^b ARIZONA STATE UNIVERSITY   (United States)

Author keywords

A stability; Fourier series method; General linear method; Least squares minimization; Ordinary differential equation; Region of stability; Runge Kutta formula

Indexed keywords

ALGORITHMS; COMPUTER AIDED ANALYSIS; CONVERGENCE OF NUMERICAL METHODS; INTEGRATION; LEAST SQUARES APPROXIMATIONS; LINEARIZATION; NONLINEAR EQUATIONS; OPTIMIZATION; POLYNOMIALS; RUNGE KUTTA METHODS;

FOURIER SERIES METHOD; GENERAL LINEAR METHOD; MULTISTAGE INTEGRATION METHODS; SOFTWARE PACKAGE MINPACK;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 0032068326     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(97)00109-8     Document Type: Article

References (8)

1. J.C. Butcher, Diagonally-implicit multi-stage integration methods, Appl. Numer. Math. 11 (1993) 347-363.
2. J.C. Butcher, General linear methods for the parallel solution of ordinary differential equations, in: World Series in Applicable Analysis 2 (1993) pp. 99-111.
3. J.C. Butcher, A transformation for the analysis of DIMSIMs, BIT 34 (1994) 25-32.
4. J.C. Butcher and Z. Jackiewicz, Diagonally implicit general linear methods for ordinary differential equations, BIT 33 (1993) 452-472.
5. J.C. Butcher and Z. Jackiewicz, Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations, Appl. Numer. Math. 21 (1996) 385-415.
6. J.C. Butcher and Z. Jackiewicz, Implementation of diagonally implicit multistage integration methods for ordinary differential equations, SIAM J. Numer. Anal. 34 (1997) 2119-2141.
7. J.E. Dennis and R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, NJ, 1983).
8. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems (Springer, Berlin, 1991).