| There are many problems can be described by the partial differential equation in the natural science and engineering technology field, studying the numeric solution of these partial differential equations is a strong tool for solving these problems. How to get the numeric solution of these partial differential equations has been become a special course and many foreigners and researchers studying in this field. All kinds of numerical methods and the last studying solutions are used to solve the technology problems. In this paper, the numerical solutions of the complex partial differential equations and nonlinear Burgers equation and nonlinear Boussinesq equation through use the difference method and MOL method.But in fact, if the operator, the right term, the boundary condition or the initial condition is not known and the solution of the equation isn't known either, the partial differential equation becomes an inverse problem. The theory and the solving solution of the inverse problem are more difficult than those of the direct problem and be related withmany aspects because the inverse problems is nonlinear and ill-posed, and how to solve these problems becomes a new field that mathematics learners, natural science researchers and engineering technology learners try to study.In this paper, we used the regularization method and the best disturbed iteration to solve such more extensive equations: every kind of positive problems and inverse problems of the hyperbolic partial differential equation and parabolic equation. We give homologous methods to solve the positive problems and inverse problems of nonlinear Burgers equation and Boussinesq equation. In the process, a new creative point of determines the initial values of unknown variety for repetition by use Genetic Algorithms is given. Therefore, a lot of numerical computed examples show that the process which above decrypted to solve the complex inverse problems has good stability and high accuracy.
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