Conjugate gradient method were choosed to solve the large sparse matrix equations induced by the FEM and computer language FORTRAN was used to programme the numerical simulation system software.

Kinetic shear Alfvn modes in tokamak plasmas (with or without temperature gradient) in the full gyrokinetic limit are numerically investigated by using the integral eigenvalue equations.

This paper is investigated a preconditioned conjugate gradient method in solving a linear algebraic system of large sparse symmetric and positive equations.