Title: A numerical method based on the Adomian decomposition method for identifying an unknown source in non-local initial-boundary value problems

Authors: Reza Pourgholi; Akram Saeedi

Addresses: School of Mathematics and Computer Sciences, Damghan University, P.O. Box 36715-364, Damghan, Iran ' School of Mathematics and Computer Sciences, Damghan University, P.O. Box 36715-364, Damghan, Iran

Abstract: Determination of an unknown time-dependent function in parabolic differential equations plays a very important role in many branches of science and engineering. In this paper, we present an approach based on ADM to solve inverse non-local initial-boundary value problems, since this problem is mildly ill-posed, the Tikhonov regularisation method is applied to deal with noisy input data and obtain a stable approximate solution. This method provides a reliable algorithm that requires less work if compared with the traditional techniques. Numerical results obtained from this method, indicating high accuracy and speed of the method.

Keywords: inverse problems; Adomian decomposition method; ADM; non-local boundary value; least squares; Tikhonov regularisation method; unknown time-dependent function; parabolic differential equations.

DOI: 10.1504/IJMMNO.2015.071869

International Journal of Mathematical Modelling and Numerical Optimisation, 2015 Vol.6 No.3, pp.185 - 197

Received: 26 Feb 2015
Accepted: 14 May 2015
Published online: 21 Sep 2015 *

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