Kamal Rashedi - Department of Mathematics, University of Science and Technology of Mazandaran, Behshahr, Iran
Fatemeh Baharifard - School of Computer Science, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran

In the current paper, we numerically investigate the approximation of a timewise-dependent heat transfer coefficient (HTC) along with the temperature in the one-dimensional heat equation with the third-type boundary conditions and an integral measurement. We utilize the integral overdetermination condition to reformulate the third-type boundary conditions and seek the solution to the converted problem in the form of the linear combination of the method of fundamental solutions and the heat polynomials. By applying the collocation method, the problem is reduced to the solution of a linear system of algebraic equations. The method takes advantage of the combination of the natural cubic spline technique and the Tikhonov regularization method to provide a stable approximation of the derivative of the perturbed boundary data. We provide several numerical tests to show the effectiveness of the proposed method.

Parabolic equation, Method Of fundamental solutions, Heat polynomials, heat transfer coefficient, Tikhonov Regularization