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Yu-Jie Ren,Fu-Gui Song,Yan-Juan Li,Hong-Qing Zhang 한국멀티미디어학회 2006 한국멀티미디어학회 국제학술대회 Vol.2006 No.-
In the paper, a new mechanization method on the mixed operation of the numerical solutions, analytic solution (if exist), and showing their figures simultaneously for differential equation and their MATLAB programs are presented. With the aid of computer software MATLAB, Euler's method is chosen to illustrate the validity and advantages of the method. As a result, we can not only see the analytic solution, numerical solutions, and their errors but also observe how step size affects the error of the numerical solutions by a figure. The mechanization method can be also applied to other numerical method.
Yu-Jie Ren,Yan-Juan Li,Fu-Gui Song,Hong-Qing Zhang 한국멀티미디어학회 2006 한국멀티미디어학회 국제학술대회 Vol.2006 No.-
In the paper, a new compound operation method of the numerical solutions and analytic solution (if exist) is proposed to constructing explicit solutions for nonlinear partial differential equations based on computation system MATLAB. The validity and reliability of the method is tested by its application to the Toda-Lattice equations in (2+1) dimensions. More new explicit solutions are found. The compound operation method can be also applied to other nonlinear partial differential equations.