Solving Initial – Value Problems by Explicit Domain Decomposition Approximate Inverses

A class of hybrid heterogeneous methods using time implicit backward differences and Crank-Nicolson approximating schemes in conjunction with explicit domain decomposition approximate inverse matrix techniques is introduced for computing various families of approximate inverses based on approximate LU-type factorization techniques. Explicit preconditioned conjugate gradient type schemes in conjunction with approximate inverse matrix techniques are presented for the efficient solution of linear systems. Application of the new proposed hybrid method on a 2D initial value problem is discussed and numerical results are given.