A Tau Method for the One-Dimensional Parabolic Inverse Problem Subject to Temperature Overspecification

In this work, an approximational technique based on shifted Legendre-tau ideas is presented for the one-dimensional parabolic inverse problem with a control parameter. The method consists of expanding the required approximate solution as the elements of a shifted Legendre polynomial. Using the operational matrices we reduce the problem to a set of algebraic equations. A numerical example is included to demonstrate the validity and applicability of the technique and a comparison is made with existing results. The method is easy to implement and produces very accurate results.