A General Coupled Equation Approach for Solving the Biharmonic Boundary Value Problem,
Abstract
The biharmonic boundary value problem with Dirichlet boundary conditions is reduced to a coupled system of Poisson equations, which depend upon an arbitrary, positive coupling constant c. Since each of the Poisson equations is well-posed, the system may be solved by iteration. The author shows that the iterates may be represented as a linear combination of the eigenfunctions of the Dirichlet eigenvalue problem. Convergence of the iterative scheme occurs when O < c< 2 nu sub 1 where nu sub 1 is the smallest eigenvalue. By making use of an averaging scheme convergence may be produced for any positive c. With the proper choice of c, the rate of convergence may be increased. This coupled equation approach includes the finite difference approach as a special case. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1971
- Accession Number
- AD0734169
Entities
People
- Johnnie W. Mclaurin
Organizations
- University of California, Los Angeles