algebraic difference
1.By using the solutions of a new auxiliary elliptic equation,a direct algebraic method is proposed to construct the exact solutions of some nonlinear evolution equations.The main difference between this method and previous auxiliary elliptic equation methods is that the balance order becomes smaller after using the new auxiliary elliptic equation.Therefore,the derived algebraic equations are greatly simplified.Meanwhile,the obtained new solutions contain more parameters to be chosen.For some special cases,they give the previous known solutions.It is shown that some new exact periodic solutions of some nonlinear evolution equations are explicitly obtained with the aid of symbolic computation.
2.In the case of large time step taken in calculation,implicit difference scheme is adopted in the discreted algebraic equations to ensure the numerical stability of the model.
3.The classic difference scheme of Euler is employed to solve the forward problem, and the truncated singular value decomposition is used to solve the ill-conditioned system of algebraic equation.
4.The discretization of the periodic solutions is adapted by the Finite Difference Method (FDM). We convert the boundary value problem (BVP) of ordinary differential equations to a system of nonlinear algebraic equations with parameters.
