Ant Colony Algorithm Study For Parabolic Equation Parameter Inversion

As known, parabolic equation is one of three kinds of partial differentialequation, and many problems in real life can be regarded as parameter inversionof Parabolic equation, so it is important to inverse the parameters of parabolicequation. In this thesis, the niche ants colony algorithm is applied to inverse theparameters of low dimensional parabolic equation and the numerical simulationresults shows that the niche ants colony algorithm is effective by comparinginversion value with true value.Firstly, we inverted four kinds of one-dimensional parabolic equation,including the identification of parameter, boundary inversion, sourceidentification problem, and the initial value inversion of one-dimensionalnon-linear parabolic equation. And then, we applied the method to solve thelocation of pollutants in the river. Lastly, we used the method to invert theparameters and source term of two-dimensional convection diffusion equationand applied it to the inversion problem of water quality model in real life. Theresults indicate advantage and effectiveness of niche ants colony algorithm.In all, we can conclude that we can use the method to solve all inversionproblems of partial differential equations, if the partial differential equations canbe solved. Therefore, some practical problems are favourite to be solvedaccording to the method.