Using an ODE solver for a class of integro-differential systems

By a simple extension of the Method of Lines, the ordinary differential equ ation solver VODPK may be used to solve a certain class of integro-differen tial equation systems (IDE systems). The problems are characterized by a pa ir of advected frequency-dependent quantities, coupled to a population vari able whose rate includes a spectral integral in one space dimension. We hav e found that with an appropriate choice of preconditioner to aid in the con vergence of the linear iterations, an extremely efficient method is obtaine d for the solution of these types of IDE system problems. We discuss the se midiscretization process and the formation of the preconditioner in some de tail. Finally, we present an application of the technique. (C) 2001 Academi c Press.