Adaptive interval wavelet precise integration method for partial differential equations. (English) Zbl 1144.65325

Summary: The quasi-Shannon interval wavelet is constructed based on the interpolation wavelet theory, and an adaptive precise integration method, which is based on extrapolation method is presented for nonlinear ordinary differential equations (ODEs). And then, an adaptive interval wavelet precise integration method (AIWPIM) for nonlinear partial differential equations (PDEs) is proposed. The numerical results show that the computational precision of AIWPIM is higher than that of the method constructed by combining the wavelet and the 4th Runge-Kutta method, and the computational amounts of these two methods are almost equal. For convenience, the Burgers equation is taken as an example in introducing this method, which is also valid for more general cases.


65T60 Numerical methods for wavelets
65L05 Numerical methods for initial value problems involving ordinary differential equations
35F30 Boundary value problems for nonlinear first-order PDEs
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