Parameter Inversion Algorithm For Nonlinear Parabolic Equations

Parameter inversion of nonlinear parabolic equations has important application value in engineering field.However,due to the nonlinearity and ill-posed nature of such problems,it is very difficult to solve them,so it is very important to find effective numerical solutions.Based on nonlinear parabolic equations,this paper focuses on the positive problem and parameter inversion problem of nonlinear parabolic equations(systems).The main research work carried out in this paper is as follows:(1)For the numerical study of nonlinear parabolic equations,the advantages and disadvantages of finite difference method,finite element method,finite volume method,boundary element method and meshless method are analyzed.In this paper,the centroid interpolation collocation method in meshless method is selected to solve the forward problem.The numerical solution obtained by this method has high accuracy and good stability.(2)For solving inverse problems of nonlinear parabolic equations(systems),a Newton regularization iterative algorithm for solving nonlinear parabolic equations(systems)is presented by analyzing the present situation and progress of inverse problems.(3)For the positive problem of one-dimensional and two-dimensional nonlinear parabolic equation(systems),a discrete process using the Barycenter interpolation method is presented,and the numerical simulation is carried out to obtain high-precision numerical solution.(4)For the inverse parameter problem of one-dimensional and two-dimensional nonlinear parabolic equations,based on the high accuracy numerical solution of the positive problem and the Newton iterative regularization algorithm,the algorithm is designed and a general parameter inversion program is compiled.Numerical simulation is carried out.The numerical results show that the proposed algorithm is feasible and effective.