Numerical method for the simultaneous determination of unknown parameters in a parabolic equation

Numerical procedures for the solution of an inverse problem of simultaneously determining unknown parameters in a linear parabolic equation are considered. The approach proposed is to approximate unknown functions using Chebyshev polynomials, which are determined consecutively from the solutions of the minimization problems based on overspecified data. Finally, the results of a numerical experiment are displayed.

[1]  Abdullah Shidfar,et al.  An inverse problem for a linear diffusion equation with non-linear boundary condition , 1989 .

[2]  Yanping Lin,et al.  An inverse problem of finding a parameter in a semi-linear heat equation , 1990 .

[3]  Abdullah Shidfar,et al.  An inverse problem for a nonlinear diffusion equation , 1997 .

[4]  Mehdi Dehghan,et al.  Finding a control parameter in one-dimensional parabolic equations , 2003, Appl. Math. Comput..

[5]  Yanping Lin,et al.  Determination of a parameter p(t) in some quasi-linear parabolic differential equations , 1988 .

[6]  R. Pourgholi,et al.  Numerical approximation of solution of an inverse heat conduction problem based on Legendre polynomials , 2006, Appl. Math. Comput..

[7]  James V. Beck,et al.  Inverse Heat Conduction , 2023 .

[8]  Mehdi Dehghan,et al.  Numerical solution of one-dimensional parabolic inverse problem , 2003, Appl. Math. Comput..

[9]  A. Shidfar,et al.  Numerical solution of inverse heat conduction problem with nonstationary measurements , 2005, Appl. Math. Comput..

[10]  A. Shidfar,et al.  An inverse heat conduction problem with a nonlinear source term , 2006 .

[11]  Zhenhai Liu.  On the identification of coefficients of semilinear parabolic equations , 1994 .

[12]  Yanping Lin,et al.  Determination of source parameter in parabolic equations , 1992 .

[13]  Zhenhai Liu.  IDENTIFICATION OF PARAMETERS IN SEMILINEAR PARABOLIC EQUATIONS , 1999 .

[14]  刘振海.  ON THE IDENTIFICATION OF COEFFICIENTS OF SEMILINEAR PARABOLIC EQUATIONS , 1994 .

[15]  Yanping Lin,et al.  A finite-difference solution to an inverse problem for determining a control function in a parabolic partial differential equation , 1989 .

[16]  J. R. Cannon,et al.  Parameter determination in parabolic partial differential equations from overspecified boundary data , 1982 .

[17]  Yanping Lin,et al.  Numerical procedures for the determination of an unknown coefficient in semi-linear parabolic differential equations , 1994 .

[18]  Yanping Lin,et al.  Determination of parameter p(t) in Holder classes for some semilinear parabolic equations , 1988 .