The resonance interaction of plasma waves with the toroidal drifts of particles leads to the occurence of a class of high order resonance integrals, which are related closed with the plasma dispersion function. Ordinary integral forms of them in finite region have been obtained by suitable complex transformation, that is very useful for their numerical calculation in case of the imaginary part of the complex parameter being small.

Numerical method for solving the free boundary plasma equilibrium equation (a nonlinear partial differential equation of elliptic type) during the evolution of the external maintaining, field is presented. The direct method is employed to solve the corresponding set of difference equation and compared with the over relaxation method.It is shown that the direct method can give better computation precision and can save considerable computer time.