The system of Ax=b where A is an n*n real matrix which is nonsingular is derived from integral equations and partial integral equations. In this paper, the method based on Krylov subspace(e.g. Arnolid,generalizedminimal residual(GMRES),bi-conjugate gradient (Bi-CG), CONJUGATE GRADIENT SQUARED (cgs) and Bi-CG stable (Bi-CGSTAB)) for solving the above linear system will be examined, then a package of software operated by 'Mathematica' concerning the previous methods will be presented, and finally I'll show the similarities among the order of operation and the time alloted and the breakdowns of those methods. Mean while, some numerical examples will be given.
