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.

This paper presents basic idea to construct high order difference schemes for linear two order ordinary differential equations with boundary values. A six order tridiagonal OCI difference scheme is deduced and the singularity at ends of interval are treated by means of limited values. A six order tridiagonal OCI difference scheme on non-uniform mesh is adopted for layer problems. A large number of numerical experimental results show that this high order tridiagonal OCI difference scheme can solve singular problems, inherent instability problems, dichotomous instability problems, singular perturbation problems and oscillating problems very well.