The local discontinuous Galerkin method for the two-dimensional equation was introduced. By introducing the auxiliary variable, the second derivative heat conduction equation equations were rewritten into first-order partial differential equations, then the discontinuous Galerkin method was applied to the system. Finally the method yields ordinary differential equations systems. The explicit method was used for the time discretization. The numerical experiments were presented to verify the accuracy of the method. 

The local discontinuous Galerkin (LDG) method using to solve poisson equations on two-dimensional domain was introduced. The construction of LDG was described. The algorithm formulation and practical implementation with linear elements and quadratic elements were discussed in triangular element cases, including numerical quadrature rules, mass matrix formula and iterative methods to solve system. At last, numerical experiments were presented to verify the accuracy of convergence.

Curve fitting method of BP neural network was introduced and applied in the model of the dispersion of calcite crystals by MATLAB tools. The results show that BP algorithm has high forecasting capacity and good generalization capacity in three areas: the map of curve fitting, the deviation curve and the error norm. BP neural network can automatically identify mathematical model, which has higher precision, and its principle is relatively simple. So it is a very good tool for complex input-output system.