Accession Number : AD0717769

Title :   An Alternate Formulation of a Method of L. V. Kantorovich.

Descriptive Note : Research rept.

Corporate Author : ALABAMA UNIV HUNTSVILLE RESEARCH INST

Personal Author(s) : Brauchli,Hans J.

Report Date : OCT 1970

Pagination or Media Count : 35

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)

Descriptors :   (*PARTIAL DIFFERENTIAL EQUATIONS, *NUMERICAL INTEGRATION), (*BOUNDARY VALUE PROBLEMS, NUMERICAL ANALYSIS), TRANSFORMATIONS(MATHEMATICS), CALCULUS OF VARIATIONS, ITERATIONS, BOUNDARY VALUE PROBLEMS

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE