Efficient numerical techniques for solving Pocklington's equation and their relationships to other methods
Abstract
The present paper shows that testing Pocklington's integrodifferential equation with piecewise sinusoids results in a system of linear integrodifference equations whose numerical solution is identical to the collocation (pointmatching) solutions of Hallen's equation for any choice of basis functions, but without the complicating arbitrary constants of integration of Hallen's equation. The wellknown piecewise sinusoidal reaction matching technique of Richmond is shown to be a special case of the proposed technique in which the basis functions are chosen to be piecewise sinusoids. Moreover, approximation of the derivative operator in Pocklington's equation by a finitedifference operator is closely similar to testing with piecewise linear (triangle) testing functions, and the resultant equation is asymptotically convergent at the same rate as Hallen's equation with pointmatching.
 Publication:

IEEE Transactions on Antennas and Propagation
 Pub Date:
 January 1976
 DOI:
 10.1109/TAP.1976.1141286
 Bibcode:
 1976ITAP...24...83W
 Keywords:

 Integral Equations;
 Linearization;
 Numerical Analysis;
 Run Time (Computers);
 Boundary Value Problems;
 Collocation;
 Convergence;
 Finite Difference Theory;
 Operators (Mathematics);
 Communications and Radar