求解 Burgers 方程的决定方程的两种方法研究

摘要

论文研究了两种求解偏微分方程的决定方程的方法，一种是运用向量场及其延拓方法，另一种是通过符号计算软件 maple 自动求解软件包。论文以 Burgers 方程为例，证明两种方法得到的结果相同。但运用 maple 自动求解软件包能够避免复杂的代数计算，提高计算的速度与准确率，适用于求解复杂的高阶非线性偏微分方程。%This paper studies two methods for solving the determining equations of partial differential equations .One is using the vector field and its extension ,the other is by automatic solution package of symbolic computation software maple . Burgers equation in the text ,for example ,proves that the two methods get the same result .But the use of maple automatic solution package can avoid complex algebraic calculations and improve the computing speed and accuracy ,which can be ap‐plied to other complex higher order nonlinear partial differential equation .