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

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.