A multipole fast asymptotic algorithm for a class of equations based on the flow function method with fractional order Laplace transform

Abstract

As a mature and reliable method, this study is based on the flow function method for mathematical modeling and establishes a class of mathematical models that are approximately realistic, flexible, and easy to calculate. According to the characteristics of fractional order calculus, the initial boundary conditions are modified and optimized to reduce the model error of this class of equations. According to the minimum energy principle and linearized integral calculation method, the multi-field multi-parameter non-linear coupling problem in the calculation process is solved, and the rapid calculation of the initial boundary model is realized. The accuracy of the model is tested by numerical simulation and simulation validation of different processes. A reliable theoretical and technical support is provided for the calculation of this type of equations.