Application Of The Interval Quasi-wavelet Numerical Method In Solving Partial Equations

In recent years, the quasi-wavelet numerical method, which is widely applied in solving the partial equations, enjoys both the globally high accuracy and the locally stability, whose theory is briefly covered in the thesis. We are interested in its mutation, that is, the interval quasi-wavelet method, which not only inherits all good features from the quasi-wavelet, but also muffles the boundary effects due to the zero extension, and which can be combined with the precise integration method so as to surpass the standard quasi-wavelet and 4th Runge-Kutta method. We herein propose the interval-quasi-wavelet-and-precise-integration method, and apply it to solve the MKDV equation and two-dimension diffusion equation, where the precise integration method is modified in solving MKDV equation so as to achieve higher accuracy. Numerical experiments demonstrate that the new method is more accurate, more stable and costs less than that of the quasi-wavelet-and-4th-Runge-Kutta method in solving two-dimension diffusion equation.