Five classes of symmetry reductions and many explicit exact solutions of BLP equations with three independent variables are given by using a direct method developed by Clarkson and kruskal.

Particle Swarm Optimization with controller for solving equations;

Application of genetic algorithm in solving equations of containing error;

This paper considers a system of reaction kinetic differential equations in the complex petroleum processing.

This paper discusses the methods for solving MESH equation groups for a distillation tower.

The sole existence of the solutions of the binary operator system of equations;

We prove the characters of A-(N){i,j…}and applications in solving the system of equations.

Introducing some common methods for the derivation of implicit function determined by system of equations: to explicitize implicit function,to differentiate equation,to use perfect differential.

High performance parallel computing of implicit LU scheme for 3D Euler equations;

A series of advection non conservative equations describing the material qualities are incorporated in the conservative Euler equations.

Based on the work of Hughes[1], a streamline upwind/Petrov-Galerkin(SUPG) weighted residual formulation is presented for the two-dimensional unsteady compressible Euler equations.

By using two extended Riccati equations and Mathematica software,the author obtains exact solutions to the Variable Coefficient Burgers Equation with forced term outside and Witham-Broer-Kaup equation,including many kinds of solitary-wave-like solutions,like periodical solutions and solitary wave solutions with variable speed,many of which are found for the first time.

By constructing one new Riccati equations and using the generalixed Riccati method,we simplified the form and enriched the general results.

By using two extended Riccati equations and Mathematica software,exact solutions Of(2+1)-dimensional Broer-kaup equations with variable coefficients are obtained.