非线性薄膜方程的差分迭代求解

Difference and Iterative Solution of Nonlinear Membrane Equation

对类似于非线性薄膜一类的非线性偏微分方程提出一种新的算法。该法首先略去非线性部分的影响,或给予非线性部分某一初值,使非线性部分成为已知,从而将原非线性方程转化为线性方程,并按差分法或其它方法求得其线性解。再将所得线性解代入非线性部分使其成为已知,再次求得其解。这样反复迭代直至收敛,进而求得原非线性方程的非线生解。

For the nonlinear partial difference equation of membrane and the like,a new solution is put forward. Firstly,the effect of the nonlinear part is neglected or an initial value is given to make the part known. The original nonlinear equation linearized this way is to be solved by differential method or other linear methods. Then the linear result is put into the nonlinear part again. The linearized equation can be solved as above once more. The iteration is repeated until a satisfied result is achieved. Finally, a solution to the original nonlinear equation is obtained by the iteration process.