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Numerical techniques for solving system of nonlinear inverse problem

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Abstract

In this paper, based on the cubic B-spline finite element (CBSFE) and the radial basis functions (RBFs) methods, the inverse problems of finding the nonlinear source term for system of reaction–diffusion equations are studied. The approach of the proposed methods are to approximate unknown coefficients by a polynomial function whose coefficients are determined from the solution of minimization problem based on the overspecified data. In fact, this work considers a comparative study between the cubic B-spline finite element method and radial basis functions method. The stability and convergence analysis for these problems are investigated and some examples are given to illustrate the results.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Damghan University, P.O. Box 36715-364, Damghan, Iran

    Reza Pourgholi, S. Hashem Tabasi & Hamed Zeidabadi

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  1. Reza Pourgholi
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  2. S. Hashem Tabasi
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  3. Hamed Zeidabadi
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Correspondence to Reza Pourgholi.

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Pourgholi, R., Tabasi, S.H. & Zeidabadi, H. Numerical techniques for solving system of nonlinear inverse problem. Engineering with Computers 34, 487–502 (2018). https://doi.org/10.1007/s00366-017-0554-6

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  • DOI: https://doi.org/10.1007/s00366-017-0554-6

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