Parameter Estimation Method For Two Class Of Partial Differential Equations

Partial differential equations that describe natural phenomena often contain unknown parameters to be determined,such as thermal conductivity,diffusion coefficient,etc.People usually do not have professional instruments to measure these coefficients.They can only measure the solutions of partial differential equations at several points.And the values at several points of the initial boundary conditions are used to estimate these unknown parameters in partial differential equations.This is the parameter estimation of partial differential equations.The parameter estimation of partial differential equations is a classical problem in the inverse problem of partial differential equations.It has a wide application field and comes from various practical backgrounds.It has attracted experts and scholars in various fields at home and abroad to discuss and discuss.In this paper,two-dimensional second-order constant-coefficient hyperbolic and parabolic equations are studied.The least-squares estimation method and ridge estimation method in multivariate linear regression analysis are combined with numerical difference theory to give two kinds of known samples.Parameter Estimation of Second Order Constant Coefficient Partial Differential Equations under the Condition of Data and Model Types.First,the parameters of the second-order second-order constant-coefficient hyperbolic equations are estimated by using the least-squares estimation method and the ridge estimation method respectively,and the parameter estimation values obtained by the two estimation methods are compared.The numerical simulation results show that when the step lengths h1 and h2 satisfy a certain relationship(this relationship is determined by the hyperbolic equation itself),the parameter of the 2D second-order constant coefficient partial differential equation based on the least square estimate is given.The estimation method can estimate the parameters of two-dimensional second-order constant coefficient hyperbolic equations;under certain combinations of step sizes,the parameter estimation method based on ridge estimation for two-dimensional second-order constant coefficient partial differential equations can be improved.The Accuracy of the Parameter Estimation of the Second Order Hyperbolic Partial Differential Equation with Constant Coefficients.Secondly,the parameters of the parabolic equation of the second-order second-order constant coefficient are estimated by using the least square estimation method and the ridge estimation method respectively,and the parameter estimation values obtained by the two estimation methods are also compared.The numerical simulation results show that when the step lengths h1 and h2 satisfy a certain specific relationship(this relationship is determined by the parabolic equation itself),the two-dimensional second-order constant coefficient partial differential equation based on the least squares estimation method is given.The parameter estimation method can estimate the parameters of a two-dimensional second-order constant coefficient parabolic equation.When the step lengths h1 and h2 do not satisfy a certain specific relationship,the ridge estimation method has a good effect on estimating the parametric equation of a second-order constant coefficient parabolic equation.The accuracy of the parameter estimation of parabolic equations with second-order constant coefficients is greatly improved.