A method based on the tau approach for the identification of a time-dependent coefficient in the heat equation subject to an extra measurement

作者：Saadatmandi Abbas; Dehghan Mehdi^*

来源：Journal of Vibration and Control, 2012, 18(8): 1125-1132.

DOI：10.1177/1077546311408474

• Diffusion equation
• extra measurement
• operational matrix
• parabolic partial differential equations
• parameter determination problem
• shifted Legendre-tau method

In this work, the problem of parameter identification in a parabolic partial differential equation is discussed. The shifted Legendre-tau method is presented for finding the unknown function and also the unknown coefficient in the one-dimensional diffusion model. The method consists of expanding the required approximate solution as the elements of a shifted Legendre polynomial and by using operational matrices we reduce the problem to a set of algebraic equations. Several examples are given to demonstrate the validity and applicability of the technique and a comparison is made with existing results. The method is easy to implement and yields very accurate results.

• 出版日期2012-7