An integral equation is developed for determining the time-dependent current distribution on a wire structure excited by an arbitrary time-varying electric field. The subsectional collocation form of the method of moments is used to reduce this integral equation to a form that can be evaluated on a digital computer as an initial value problem. A Lagrangian interpolation scheme is introduced so that the dependent variables can be accurately evaluated at any point in the spacetime cone; thus, only mild restrictions on the space and time sample density are required. The integral equation relating present values of the current to previously computed values is presented in a form that can be directly converted into a computer code. Expressions are developed for the computer time and the relative advantages of time-domain and frequency-domain calculations are discussed, providing impetus for analyses in the time domain in certain cases. Part 11 of this paper will present well-validated numerical results obtained using the technique described. © 1973.
Miller, E. K., Poggio, A. J., & Burke, G. J. (1973). An integro-differential equation technique for the time-domain analysis of thin wire structures. I. The numerical method. Journal of Computational Physics, 12(1), 24–48. https://doi.org/10.1016/0021-9991(73)90167-8