Numerical simulation of dynamic behaviour of internal transport with a barrier trigger in Tokamak plasmas in splitting domain and its parallel computation are shown.The parallel efficiency increases with the computing scale.Numerical results agree well with theoretical analysis.The code adapts to the simulation of nonlinear tearing mode (specially mutiple mode) as well.

The strong dependence of fusion reaction rate on ion temperature leads to a thermalinstability of D T burning plasma.Mathematical qualites are discussed for the non-linear differential equations describing the steady state power balance of a D T burning plasma.Shooting method is used to obtain equilibrium solution and eigenvalue of the linearized equation about temperature pertubation around equilibrium.How ever,the solution obtained by the above method can be different from the time-dependent one for t→∞.This provides a typical example of a kind of unsolved non-linear mathematical problem.

A numerical code has been established for solving self-consistent equilibrium equation and calculating the dependence of the tearing mode on the current density profile. The external belieal field effect is included in it.The dynamic alternating direction implicit method is applied to speed up the convergence of solution of equilibrium equation and three-point difference secheme is taken to solve the singular boundary value problem with two singular points.

A set of nonlinear second order parabolic partial differential equations with initial-boundary values is approxinated by Crank-Nicholson difference method, and successfully solved by means of Loop-Iteration method. The computation of energy transport in tokamak plasma by ohmic heating provides numerical results in agreement with the theoretial analysis.

This paper describes a method for computing highly oscillatory integrals with the Mathieu function. The practice proves that not only the results are highly satisfactory, but also the method is time-saving.

A kind of singular boundary value problems for second order systems with a singularity at the origin and a non-normal singularity at the resonance layer are solved by means of the three-point difference method. Comparing with the method proposed by Ross et al.,_[1] the present method is not only computationally simpler and more distinct but also can save much computer time. Our numerical results are in agreement with those given in Ref. 1.