Numerical new algorithm of PDEs based on the second generation wavelet

Based on characteristics of high computational efficiency and with realization adaptation easy the second generation wavelet transform,differential equation 's numerical resolution is mapped to wavelet coefficient space,then reference the wavelet coefficient to choose the appropriate threshold for constructing adaptive mesh.In the region corresponding to wavelet coefficients that are greater than the threshold,the wavelet function's scale is increased appropriately and the resolution of basis functions is improved,so that the abrupt structure of numerical resolution can be captured by the method;meanwhile,inverse wavelet transform is introduced into the approximation process of the numerical solution to avoid the direct operation on the wavelet basis and improve the execution efficiency of the algorithm.Derivatives of spatial variable are calculated using the finite difference method with variable step size on the adaptive mesh,the equation is solved iteratively by forward difference in time direction.