Preconditioned techniques for solving large sparse linear systems arising from the discretization of the elliptic partial differential equations

In this paper, we use the BiCG, BiCGSTAB methods as preconditioned techniques. Also we compare the preconditioned Krylov subspace methods such as GMRES, GMRES(m), QMR, BiCG, CGS, BiCGSTAB for solving linear systems arising from a class of fourth-order approximations for solving the elliptic partial differential equation Auxx + Buyy = f(x, y, u, ux, uy), where A and B are constants. Numerical results are given to show the efficiency of the proposed preconditioned BiCGSTAB method.