Numerical Solutions of Electromagnetic Boundary Value Problems by Means of the Asymptotic Anticipation Method

A method for improving the accuracy of approximate numerical solutions of doubly infinite sets of simultaneous linear algebraic equations is presented. The method is based on using prior information about the asymptotic behavior of the solution to anticipate the dominant contribution of the terms beyond the truncation limit imposed by the restriction of numerical solutions to finite matrix equations. Such information is shown to be available for the sets of equations which are frequently used in electromagnetic boundary value problems. The advantages and disadvantages of this method are discussed and then illustrated via results for the well‐known problem of scattering from a planar grating.