A method of lines framework in Mathematica

Journal of Numerical Analysis, Industrial and Applied Mathematics

Volumn 3, Issue 1-2, 2008, Pages 43-59

  Knapp, R ^a  

^a WOLFRAM RESEARCH INC   (United States)

Author keywords

Method of lines; MOL

Indexed keywords

EID: 62649127687     PISSN: 17908140     EISSN: 17908159     Source Type: Journal    
DOI: None     Document Type: Article

References (23)

1. F. Bornemann, D. Laurie, S. Wagon, J. Waldvogel, The SIAM 100-Digit Challenge, SIAM Books, 2004.
2. J. P. Boyd, Chebyshev and Fourier Spectral Methods Second Edition, Dover, 2001.
3. B. Fornberg, Fast Generation of Weights in Finite Difference Formulas, in Recent Developments in Numerical Methods and Software for ODEs/DAEs/PDEs (G.D. Byrne and W.E. Schiesser, Eds), World Scientific, 1992.
4. B. Fornberg, A Practical Guide to Pseudospectral Methods, Cambridge University Press, 1996.
5. B. Fornberg, Calculation of weights in finite difference formulas. SIAM Review 40 No. 3, 1998.
6. A. Harten, B. Engquist, S. Osher, and S. R. Chakravarthy, Uniformly high-order accurate essentially nonoscillatory schemes, Journal of Computational Physics, 71, 1987.
7. A. C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, in Scientific Computing, (R. S. Stepleman et al. Eds.), North-Holland, Amsterdam, 1983.
8. Hindmarsh, Alan C., and A. G. Taylor, User Documentation for IDA, a Differential-Algebraic Equation Solver for Sequential and Parallel Computers, Lawrence Livermore National Laboratory technical manual UCRL-MA-136910, December 1999.
9. J.M. Hyman, R.J. Knapp, and J.C. Scovel, High Order Finite Volume Approximations of Differential Operators on Nonuniform Grids, in Experimental Mathematics: Computational Issues in Nonlinear Science (J.M. Hyman, Ed.), North Holland, 1992.
10. R. Knapp, M. Sofroniou, S. Wolfram, et. al., Advanced Numerical Differential Equation Solving in Mathematica, http://reference.wolfram.com/mathematica/tutorial/NDSolveOverview.html
11. H. J. Lee and W. E. Schiesser, Ordinary and Partial Differential Equation Routines in C, C++, Fortran, Java, Maple and Matlab, CRC Press, Boca Raton, FL, 2004
12. X.D. Liu, S. Osher, and T. Chan, Weighted Essentially Nonoscillatory Schemes, Journal of Computational Physics, 115 1994.
13. K. Radhakrishnan and A. C. Hindmarsh, Description and Use of LSODE, the Livermore Solver for Ordinary Differential Equations, LLNL report UCRL-ID-113855, December 1993.
14. W.E. Schiesser, The Numerical Method of Lines, Academic Press, 1991.
15. L. N. Trefethen, Spectral Methods in Matlab, SIAM, Philadelphia, 2000.
16. L. N. Trefethen, The $100 100-Digit Challenge, SIAM News 35 no. 6 1-3, 2002.
17. A. Vande Wouwer, P. Saucez and W. E. Schiesser (eds.), Adaptive Method of Lines, CRC Press, Boca Raton, FL, 2001
18. A. Vande Wouwer, P. Saucez and W. E. Schiesser, Simulation of Distributed Parameter Systems Using a Matlab-based Method of Lines Toolbox, Ind. Eng. Chem. Res., 43, pp 3469-3477, 2004
19. A. Vande Wouwer and W. E. Schiesser (eds.), J. Computational and Applied Mathemtics (special issue on the method of lines), 183, no. 2, 15 November 2005
20. S. Wolfram, A New Kind of Science, Wolfram Media, Inc., 2002
21. S. Wolfram, et. al., Mathematica Documentation, http://reference.wolfram.com/
22. S. Wolfram, Nonlinear Wave Equation Explorer, from The Wolfram Demonstrations Project http://demonstrations.wolfram.com/NonlinearWaveEquationExplorer
23. S. Wolfram, et. al., NDSolve reference page, http://reference.wolfram.com/mathematica/ref/NDSolve.html