The improved Boussinesq equation is solved with classical finite element method using the most basic Lagrange element k = 1, which leads us to a second order nonlinear ordinary differential equations system in time;th...The improved Boussinesq equation is solved with classical finite element method using the most basic Lagrange element k = 1, which leads us to a second order nonlinear ordinary differential equations system in time;this can be solved by any standard accurate numerical method for example Runge-Kutta-Fehlberg. The technique is validated with a typical example and a fourth order convergence in space is confirmed;the 1- and 2-soliton solutions are used to simulate wave travel, wave splitting and interaction;solution blow up is described graphically. The computer symbolic system MathLab is quite used for numerical simulation in this paper;the known results in the bibliography are confirmed.展开更多
文摘The improved Boussinesq equation is solved with classical finite element method using the most basic Lagrange element k = 1, which leads us to a second order nonlinear ordinary differential equations system in time;this can be solved by any standard accurate numerical method for example Runge-Kutta-Fehlberg. The technique is validated with a typical example and a fourth order convergence in space is confirmed;the 1- and 2-soliton solutions are used to simulate wave travel, wave splitting and interaction;solution blow up is described graphically. The computer symbolic system MathLab is quite used for numerical simulation in this paper;the known results in the bibliography are confirmed.
