Survey of Temporal Basis Functions for Integral Equation Methods

To make the implicit marching-on-in-time schemes stable for practical applications, choices of appropriate temporal basis functions are investigated. The quadratic and cubic cardinal B-spline functions are introduced as new time bases for which the numerical solution of the electric field integral equation demonstrates that they can compete with the time shifted Lagrange interpolating functions in terms of accuracy and stability. It is shown that especially for small time step sizes using the analytical closed-form derivatives of the bases tremendously enhance the extension of the stable region in comparison with the results obtained using available consistent integrator-interpolator pairs.