Boundary value problems for the laplacian in the Euclidean space solved by symbolic computation
By means of the symbolic manipulation language REDUCE, a complete set of harmonic polynomials in Euclidean space is constructed. The method relies on the theory of monogenic functions defined in ℝn+1 and taking values in a Clifford algebra An. An approximate solution for the Dirichlet and Neumann problems in the form of a harmonic polynomial may be obtained. The method is applied to solying a Dirichlet problem in a cube.
Unable to display preview. Download preview PDF.
- R.W. WILKERSON, Symbolic Computation and the Dirichlet problem, Eurosam 84, Lecture Notes in Computer Science 174, 59–63.Google Scholar
- S. ZAREMBA, L'équation biharmonique et une classe remarquable de fonctions fondamentales harmoniques, Bull. Inter. de l'Acad. Scie. de Cracovie (1907), 147–196.Google Scholar
- J. WALSH, The approximation of harmonic functions by harmonic polynomials and by harmonic rational functions, Amer. Math. Soc. Bull. 35 (1929), 499–544.Google Scholar
- F. BRACKX, R. DELANGHE and F. SOMMEN, Clifford Analysis, Pitman London, 1982Google Scholar
- F. BRACKX, D. CONSTALES, R. DELANGHE and H. SERRAS, Clifford Algebra with REDUCE, Rend. Circ. Mat. Palermo, Ser. II, 16, (1987), 11–19.Google Scholar