On the choice of expansion and weighting functions in the numerical solution of operator equations
- 1 September 1985
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Antennas and Propagation
- Vol. 33 (9), 988-996
- https://doi.org/10.1109/tap.1985.1143707
Abstract
One of the objectives of this paper is to discuss the mathematical requirements that the expansion functions must satisfy in the method of moments (MM) solution of an operator equation. A simple differential equation is solved to demonstrate these requirements. The second objective is to study the numerical stability of point matching method, Galerkin's method, and the method of least squares. Pocklington's integral equation is considered and numerical results are presented to illustrate the effect of various choices of weighting functions on the rate of convergence. Finally, it is shown that certain choices of expansion and weighting functions yield numerically acceptable results even though they are not admissible from a strictly mathematical point of view. The reason for this paradox is outlined.Keywords
This publication has 7 references indexed in Scilit:
- A note on the choice weighting functions in the method of momentsIEEE Transactions on Antennas and Propagation, 1985
- A note on the variational method (Rayleigh-Ritz), Galerkin's Method, and the method of least squaresRadio Science, 1983
- A study of the various methods for computing electromagnetic field utilizing thin wire integral equationsRadio Science, 1983
- Some mathematical considerations in dealing with the inverse problemIEEE Transactions on Antennas and Propagation, 1981
- The Use of Collocation as a Projection Method for Solving Linear Operator EquationsSIAM Journal on Numerical Analysis, 1972
- Approximate Solution of Operator EquationsPublished by Springer Nature ,1972
- Matrix methods for field problemsProceedings of the IEEE, 1967