中文摘要：

对小波理论在偏微分方程数值求解中的应用进行深入研究的基础上,提出了一种自适应求解非线性偏微分方程的算法——小波最优有限差分法。并以非线性Burgers方程为例,分别用小波最优有限差分法和直线法对它进行数值求解,显示了小波最优有限差分法在数值求解非线性问题时的自适应性、高效性和可行性。

英文摘要：

In the foundation of thorough studies on wavelet theory and its applications in numerical solution of partial differential equation, a adaptive wavelet algorithm for numerical solution of partial differential equation-wavelet optimized finite difference method is advanced.The nonlinear Burgers equation is taken as an example, WOFD and method of lines are used to solve it,it turns out that the WOFD has adaptability,high efficiency and feasibility.