Summarizing the Method of Solution of the Majority of Differential Equation by Using Tensor Product B-Spline Wavelet Scaling Functions in Network Security and Software Security Area, the Imitating Von Neumann Stability Analysis and a Typical Example

In order to obtain fast solution of differential equations, as an example, detailed process of the solution of one-dimensional differential equation using B-spline wavelet scaling function is proposed to demonstrate the transformation of the high-order temporal derivative to one-order temporal derivative, linearization of the nonlinear equation, the relationship between the condition number used for measuring the degree of matrix's ill-condition and the number of order of spatial derivative, we explain the reason that three-dimensional diffusion equation was selected as a typical example of numerical calculation, using this typical example to illustrate that the method we enploged is obviously better than the difference method. The calculations from a case history indicate that the method provides high accuracy and the computational efficiency is enhanced due to the small matrix derived from this method. Finally, the paper also introduces a kind of new stability analyzing-method for the solution of the typical example using wavelet scaling functions.