Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2

Parabolic Equations Related Publications

2 Recovering the Boundary Data in the Two Dimensional Inverse Heat Conduction Problem Using the Ritz-Galerkin Method

Authors: Kamal Rashedi, Saeed Sarabadan

Abstract:

This article presents a numerical method to find the heat flux in an inhomogeneous inverse heat conduction problem with linear boundary conditions and an extra specification at the terminal. The method is based upon applying the satisfier function along with the Ritz-Galerkin technique to reduce the approximate solution of the inverse problem to the solution of a system of algebraic equations. The instability of the problem is resolved by taking advantage of the Landweber’s iterations as an admissible regularization strategy. In computations, we find the stable and low-cost results which demonstrate the efficiency of the technique.

Keywords: Inverse problem, Parabolic Equations, heat equation, Ritz-Galerkin method, Landweber iterations

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1 A New Algorithm for Determining the Leading Coefficient of in the Parabolic Equation

Authors: Shiping Zhou, Minggen Cui

Abstract:

This paper investigates the inverse problem of determining the unknown time-dependent leading coefficient in the parabolic equation using the usual conditions of the direct problem and an additional condition. An algorithm is developed for solving numerically the inverse problem using the technique of space decomposition in a reproducing kernel space. The leading coefficients can be solved by a lower triangular linear system. Numerical experiments are presented to show the efficiency of the proposed methods.

Keywords: Parabolic Equations, coefficient inverse problem, reproducing kernel

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