由相容性求任意阶非线性偏微分方程的决定方程

The determining equations for the nonclassical method of the nonlinear differential equation with arbitrary order can be obtained through the compatibility

研究了求任意阶的非线性偏微分方程的决定方程,运用相容性方法,和运用传统的向量场及其延拓的方法求得的结果相同.但运用相容性方法不用再计算复杂的无穷小生成元的延拓的系数,这样在计算过程中既能提高计算的速度,又能提高计算的准确率,因此,这种方法比运用向量场及其延拓的方法更简便、快捷,并举例验证了这一事实.

We investigate the determining equations for the nonlinear differential equations with arbitrary order ,the results which are obtained through the method of compatibility and the classical method of vector field and its prolong are the same. But use of the method of compatibility ,we should not compute the complex coefficient of the prolong of the infinitesimals,thus the speed and accuracy of calculation are improved.So,the method is faster and simpler than the method of vector field and its prolong,and also,we have exemplified this.