An Alternate Formulation of a Method of L. V. Kantorovich.
Abstract
In his method to reduce a partial differential equation to a system of ordinary differential equations, Kantorovich uses a cartesian coordinate as an independent variable. For partial differential equations arising from variational problems, an alternate formulation is presented, wherein an arbitrary function takes the role of the independent variable. This procedure should allow the subspace approximating the solution to be adapted to the problem at hand. The differential equations are put in a form to minimize regularity conditions on the base functions, e.g., for a second order differential equation, piecewise linear base functions will be admitted. The set of admissible base functions will be dependent on the boundary conditions of the problem. Iterative methods to solve the corresponding two-point boundary value problem are discussed. Examples presented include Poisson's equation and the biharmonic equation. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1970
- Accession Number
- AD0717769
Entities
People
- Hans J. Brauchli
Organizations
- University of Alabama in Huntsville