INTERPOLATION WITH POLYNOMIALS TO BOUNDARY VALUES.
Final scientific rept. 1 Aug 66-31 Jul 68,
MIAMI UNIV CORAL GABLES FLA DEPT OF MATHEMATICS
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The paper is the Final Scientific Report for research under the above titled grant. The central theme of the project supported by the grant is research into the theory and practically of solving boundary value problems in applied mathematics by what Collatz calls the method of collocation. The method consists in taking functions of a simple type here polynomials which satisfy a given underlying partial differential equation, and forcing them to coincide with the boundary data at various points chosen on the boundary. The central question for mathematical research is as follows By properly spacing the interpolation points and by indefinitely increasing their number, is it possible to make the corresponding sequence of simple functions approach the solution of the boundary value problem throughout the region enclosed by that boundary. The type of boundary value problem on which this project is focused is the Dirichlet Problem. Author
- Theoretical Mathematics