A new sequence of eigenfunctions is developed and studied in depth. These theta polynomials are derived from a recent analytic solution of the canonical Cauchy problem for parabolic equations, namely, the inverse heat conduction problem. By appealing to the methods of the operator calculus, it is possible to categorize the new functions as polynomials of binomial and Sheffer types. The connecti...

in this paper, we investigate the application of the homotopy perturbation method (hpm) for solving a one-dimensional nonlinear inverse heat conduction problem. in this problem the thermal conductivity term is a linear function with respect to unknown heat temperature in bounded interval. furthermore, the temperature histories are unknown at the end point of the interval. this problem is ill-po...

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. ...

In the heat conduction problems if the heat flux and/or temperature histories at the surface of a solid body are known as functions of time, then the temperature distribution can be found. This is termed as a direct problem. However in many heat transfer situations, the surface heat flux and temperature histories must be determined from transient temperature measurements at one or more interior...

(Received July 12, 2009, accepted September 3, 2009) Abstract. In this paper we consider a numerical approach for the determination of an unknown boundary condition in the inverse heat conduction problem (IHCP). The given heat conduction equation, the boundary condition, and the initial condition are presented in a dimensionless form. The numerical algorithm based on finite-difference method an...

We propose in this paper an effective meshless and integration-free method for the numerical solution of multidimensional inverse heat conduction problems. Due to the use of fundamental solutions as basis functions, the method leads to a global approximation scheme in both the spatial and time domains. To tackle the ill-conditioning problem of the resultant linear system of equations, we apply ...