【摘要】 提出了一种新的求解偏微分方程 (PDE)的全方向快速小波配置法 (FWCM) .通过用 x方向的 B-样条小波基函数同时表示 x方向与 t方向的未知函数导数 ,实现了全方向的离散小波变换 .与原先只对 x方向进行小波变换的 FWCM相比 ,此算法能更有效地利用小波的局部性与自适应性 ,从而更有效地求解 PDE.同时它还具有很好的通用性 ,可应用于求解各种类型的 PDE.更多还原

【Abstract】 A novel omnidirectional fast wavelet collocation method (FWCM) is proposed to solve partial differential equations (PDE).It carries out wavelet transform in all directions by expressing derivatives in both x direction and t direction with B-spline wavelet basis in x direction.Compared with the original FWCM which only carry out wavelet transform in x direction,the proposed method can utilize the locality and adaptivity of wavelet more efficiently,consequently it can solve the PDE more efficiently.Moreover,the proposed method has good generality and can be applied to all kinds of PDE.更多还原