References

 

• weighted residual method, replacement of the solution by its approximation, minimization of the residual error

  R. Zippel. Symbolic/numeric techniques in modeling and simulation. In B. Donald, D. Kapur, and J. Mundy, editors, Symbolic and Numerical Computation in Artificial Intelligence. Academic Press, 1992.

• finite element methods

  P. S. Wang. FINGER: A symbolic system for automatic generation of numerical programs in finite element analysis. J. Symb. Comp., 2(3):305-316, 1986.

• finite difference methods

  M. C. Wirth. On the Automation of Computational Physics. PhD thesis, Lawrence Livermore National Laboratory, Livermore, 1980. UCRL-52996.

  S. Steinberg and P. J. Roache. Symbolic manipulation and computational fluid dynamics. J. Comp. Phys., 57:251-284, 1985.

  G. O. Cook Jr. ALPAL: a program to generate physics simulation codes from natural descriptions. Int. J. Mod. Phys. C, 1(1):1-51, 1990.

  R. Liska and L. Drska. FIDE: A REDUCE package for automation of FInite difference method for solving pDE. In S. Watanabe and M. Nagata, editors, Proceedings of ISSAC'90, 169-176, New York, 1990. ACM Press, Addison Wesley.

• numerical code generation

  B. L. Gates. A numerical code generation facility for REDUCE. In B. W. Char, editor, Proceedings of SYMSAC '86, 94-99, Waterloo, 1986. ACM.

  N. Sharma and P. Wang. Symbolic derivation and automatic generation of parallel routines for finite element analysis. P. Gianni, editor, Proceedings of ISSAC'88, 33-56, Berlin, 1988. Springer-Verlag.

• IRENA-interface to the numerical library (NAG, REDUCE)

  M. C. Dewar and M. G. Richardson. Reconciling symbolic and numeric computation in a practical setting. In A. Miola, editor, Proceedings of DISCO'90, 195-204, Berlin, 1990. Springer-Verlag.