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Approximate solutions of boundary-value problems using computer algebra software

R. Barrère
A. Carmasol
Organization: Ecole Nationale Supérieure d'Ingénieurs de Metz-Ile du Saulcy, France
Journal / Anthology

Mathematics with Vision: Proceedings of the First International Mathematica Symposium
Year: 1995
Page range: 45-52

The recent development of computer algebra systems and symbolic programming languages gives new insights into scientific computing: symbolic computations will now be able to serve as a substitute for numerical computations. The Galerkin procedure applies to boundary value problems from continuum physics. It is based upon a variational formulation of the initial problem and consists in computing approximate solutions as linear combinations of previously chosen basis functions. Thanks to computer algebra, symbolic basis functions can be manipulated, thus providing an alternative to the finite element technique.

*Applied Mathematics > Numerical Methods
*Mathematics > Calculus and Analysis > Differential Equations