Numerical techniques for solving system of nonlinear inverse problem. (July 2018)

• Record Type: Journal Article
• Authors: Pourgholi, Reza; Tabasi, S.; Zeidabadi, Hamed
• Is Part Of: Engineering with computers. Volume 34:Number 3(2018)
• Page Start: 487
• Page End: 502
• Publication Date: 2018-07
• Subjects: Cubic B-spline -- Finite element method -- Radial basis functions method -- Inverse problems -- Stability analysis -- Convergence analysis -- Tikhonov regularization method -- Ill-posed problems -- Noisy data -- 65M32 -- 35K05 -- 35K40; Engineering design -- Data processing -- Periodicals; Computer-aided design -- Periodicals; Conception technique -- Informatique -- Périodiques; Conception assistée par ordinateur -- Périodiques; Electronic journals; 620.00285
• DOI: 10.1007/s00366-017-0554-6
• Languages: English
• ISSNs: 0177-0667

Abstract

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.