论文信息 - An Automatic Symbolic-Numeric Taylor Series ODE Solver

An Automatic Symbolic-Numeric Taylor Series ODE Solver

One of the basic techniques in every mathematician’s toolkit is the Taylor series representation of functions. It is of such fundamental importance and it is so well understood that its use is often a first choice in numerical analysis. This faith has not, unfortunately, been transferred to the design of computer algorithms.

James H. Davenport | Brian J. Dupée | J. Davenport | B. Dupée

[1] George F. Corliss,et al. Solving Ordinary Differential Equations Using Taylor Series , 1982, TOMS.

[2] David Barton,et al. The Automatic Solution of Systems of Ordinary Differential Equations by the Method of Taylor Series , 1971, Computer/law journal.

[3] David Barton,et al. On Taylor Series and Stiff Equations , 1980, TOMS.

[4] Stephen Wolfram,et al. The Mathematica book (3rd ed.) , 1996 .

[5] Stephen Wolfram,et al. The Mathematica Book , 1996 .

[6] A. C. Norman,et al. Computing with Formal Power Series , 1975, TOMS.

[7] A. C. Norman,et al. Expanding the Solutions of Implicit Sets of Ordinary Differential Equations in Power Series , 1976, Comput. J..

[8] André Heck. Introduction to Maple (2nd ed.) , 1996 .

[9] D. Zwillinger. Handbook of differential equations , 1990 .

[10] André Heck,et al. Introduction to Maple , 1993 .

[11] Richard D. Jenks,et al. AXIOM: the scientific computation system , 1992 .

[12] Kevin A. Broughan,et al. Some symbolic computing links to the NAG numeric library , 1991, SIGS.

[13] James H. Davenport,et al. An Intelligent Interface to Numerical Routines , 1996, DISCO.

[14] Grant Keady,et al. Production of argument subprograms in the AXIOM-NAG link: examples involving nonlinear systems , 1994 .

[15] John Rischard Rice,et al. Mathematical Software , 1971 .