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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.
65T60Wavelets (numerical methods)
65L05Initial value problems for ODE (numerical methods)
35F30Boundary value problems for first order nonlinear PDE
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