Parameter Estimation Method For The Third Kind Of Boundary Conditions For A Class Of Parabolic Equations

The boundary value problem of parabolic equations has been widely used in many fields.In practice,boundary conditions often contain unknown parameters,so the study of parameter estimation methods in boundary conditions has important practical value.This paper takes the third type of boundary conditions of a class of parabolic equations as the research object,and combines the least squares theory and the ridge estimation method in multivariate linear regression analysis with the difference theory to give a parabolic type under the conditions of known sampling data.Parameter estimation method of the third kind of boundary conditions of the equation.First,this paper uses the theory of least squares estimation,combined with the difference idea,to derive the parameter estimation formulas for the third type of boundary conditions of a class of parabolic equations.Through two examples,the numerical simulation is performed.The research results show that the choice of step size determines the size of the error.When h1=h2=h and h=0.001,the relative error of the parameter k and q are the smallest.If h1=0.01 and h2=0.002 are fixed,the relative errors of the parameters k and q are the smallest.If h2=0.01 and h1=0.005 are fixed,the relative errors of the parameters k and q are the smallest.Secondly,this paper uses the ridge estimation theory and the difference idea to derive the parameter estimation formulas for the third type of boundary equations of a class of parabolic equations.Based on the least square estimation method,the effect of biased estimation on the estimation results is considered.Comparing and analyzing the accuracy of two estimation methods when ? takes different values.The research results show that the ridge estimation method can effectively reduce the error when different combinations of step sizes are selected.When ? takes an appropriate value,the result of the ridge estimation is better than the optimal estimation result of the least squares estimation.Finally,this paper presents a test method.By using the parabolic equations and the boundary conditions of the parabolic equations obtained by the estimation method,the approximate value of each node in the middle is deduced using the difference format and compared with the sample value h to test the Effectiveness of the method.The simulation analysis of an example shows that the test method is feasible.Different difference formats have a certain effect on the test results.