基于Adomian分解法的变系数组合KdV方程的近似解

Approximate solutions to the variable coefficient combined KdV equation via the Adomian decomposition method

运用Adomian分解法研究带有初值条件的变系数组合KdV方程的近似解.首先,对变系数组合KdV方程进行约化,然后对方程中的非线性项进行线性化处理,再运用Adomian分解法求出方程的四级近似解.最后在特殊情形下运用数值模拟的方法对近似解和精确解进行了误差估计,并给出了近似解和精确解的数值模拟图.

This scheme was firstly developed to obtain the approximate solution to the variable coefficient combined KdV equation with initial condition via the Adomian decomposition method.First of all,the variable coefficient combined KdV equation would be simplified,and the nonlinear term linearization in the equation would be processed,then the Adomian decomposition method would be employed to find the fourth approximate solution to the equation.Finally,in special cases using numerical simulation method estimated the error of the approximate solution and exact solution,and gave the numerical simulation diagram of the approximation solution and exact solution.