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Method of lines solutions of the parabolic inverse problem with an overspecification at a point

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Abstract

The present work is motivated by the desire to obtain numerical solution to a quasilinear parabolic inverse problem. The solution is presented by means of the method of lines. Method of lines is an alternative computational approach which involves making an approximation to the space derivatives and reducing the problem to a system of ordinary differential equations in the variable time, then a proper initial value problem solver can be used to solve this ordinary differential equations system. Some numerical examples and also comparison with finite difference methods will be investigated to confirm the efficiency of this procedure.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran, 15914, Iran

    Mehdi Dehghan & Fatemeh Shakeri

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  1. Mehdi Dehghan
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  2. Fatemeh Shakeri
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Correspondence to Mehdi Dehghan.

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Dehghan, M., Shakeri, F. Method of lines solutions of the parabolic inverse problem with an overspecification at a point. Numer Algor 50, 417–437 (2009). https://doi.org/10.1007/s11075-008-9234-3

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