解非线性偏微分方程的插值小波算法

Interpolating wavelet method for solving nonlinear partial differential equations.

利用集小波分解和分形压缩变换思想构造了与标准小波具有类似尺度特点的连续插值小波基,给出了一维和二维空间中的插值型小波函数例子.利用集小波分解集和基函数的插值性质获得了由集小波分解点确定的积分公式,使非线性部分计算量由随尺度的平方增长关系变为线性增长关系.为说明方法的可行性,最后结合New-ton迭代法给出了一个数值例子.

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 ba- sis functions are applied to obtain knot oriented quadrature rules. A numerical example, confirming the applicability of our scheme, is presented.