A time marching integral equation method for unsteady state problems Original Research Article

A time marching integral equation method is developed for solving three classes of differential equations—elliptic, hyperbolic and parabolic with the elliptic equation as the steady state limiting case of hyperbolic or parabolic equations. The method described is semi-analytical with its numerical aspect in the time discretization of the differential equation and the space discretization of the integral equation and its analytical aspect in the derivation of the integral equation via the Greenʹs function method. The analyses of the time marching integral equation for three limiting cases indicate that both the steady integral equation and the explicit algorithm are special cases of the time marching integral equation. Finite element ideas have been used to discretize the derived integral equations. Some physical problems are analysed to illustrate the method and demonstrate its reliability and efficiency.