The equation of motion is given for an integrable model of two dimensional gravity with bosonic string coupling in Riemann-Cartan space.Numerical solutions are obtained by means of numerical integraiton method and their motion curves are also shown.

Three-point center difference scheme is employed to solve tearing mode equations which have the second-order removing singularity at an interval end and the first-order non-removing sigularity on the rational magnetic surface in the interval. A method of approximately equivalent grids is presented. The numerical simulations of the tearing mode equations with toroidal coupling are done under different safety factor distributions, and give the corresponding link parameters which can determine the stability of the mode, coupling intensity parameters, growing factors. These numerical results show that the toroidal coupling effect in linear stage has a little influence.

The paper dercribes a numerical method for the resistivity gradient driven turbulence in the Tokamak edge. The mode selection for the mode-mode coupling or nonlinear interaction is discussed. The corresponding computer code for three-dimension magnetic hydrodynamics equations has been constructed, which can save the computation time effectively.

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.