AN INVESTIGATION OF A NEW CLASS OF LINEAR FINITE DIFFERENCE OPERATORS TO BE USED IN SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS.
Abstract
A new technique for constructing 'computational molecules' for linear finite difference operators is developed. The basic approach is one of approximating a two dimensional surface with a geometrically consistent interpolating polynomial of degree four or five. The desired finite difference operator is then developed from the polynomial. The resulting molecules are geometrically consistent and may be used to solve boundary value problems without the use of fictitious points. Molecules for the biharmonic operator with various boundary conditions included are presented in the paper, as well as molecules representing the boundary conditions for shear and moment along the free edge of a plate. The integrity of the molecules presented is proven by comparison of solutions for flat plate bending problems by finite difference with exact solutions from the literature. Convergence plots for each problem are also presented. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1970
- Accession Number
- AD0709095
Entities
People
- Gerald Frietas Dias
Organizations
- Naval Postgraduate School