Interpolating wavelet method for solving nonlinear partial differential equations.
Jingfen Zhu · Journal of Zhejiang University(Science Edition) · 2007
There is interpolation wavelet scheme for solving nonlinear partial differential equations.By using set wavelet decomposition and contraction fractal transforms,interpolation wavelets basis which have the same scale properties as standard wavelet basis is constructed and interpolation wavelet functions in one dimension and two dimension spaces is given.To overcome the problems of nonlinearity,set wavelet decomposition and properties of basis functions are applied to obtain knot oriented quadrature rules.A numerical example,confirming the applicability of our scheme,is presented.