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Articles

Pseudospectral method for a one-dimensional fractional inverse problem

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Pages 968-987 | Received 14 Feb 2019, Accepted 13 Oct 2019, Published online: 13 Nov 2019

References

  • Yousefi SA, Dehghan M. Legendre multiscaling functions for solving the one-dimensional parabolic inverse problem. Numer Methods Partial Differ Equ. 2009;25:1502–1510. doi: 10.1002/num.20430
  • Wang W, Han B, Yamamoto M. Inverse heat problem of determining time-dependent source parameter in reproducing kernel space. Nonlinear Anal Real World Appl. 2013;1:875–887. doi: 10.1016/j.nonrwa.2012.08.009
  • Ashpazzadeh E, Lakestani M, Razzaghi M. Cardinal Hermite interpolant multiscaling functions for solving a parabolic inverse problem. Turk J Math. 2017;41:1009–1026. doi: 10.3906/mat-1609-3
  • Rashedi K, Adibi H, Dehghan M. Determination of space-time-dependent heat source in a parabolic inverse problem via the Ritz-Galerkin technique. Inverse Probl Sci Eng. 2014;22:1077–1108. doi: 10.1080/17415977.2013.854354
  • Mohebbi A, Dehghan M. High-order scheme for determination of a control parameter in an inverse problem from the over-specified data. Comput Phys Commun. 2010;181:1947–1954. doi: 10.1016/j.cpc.2010.09.009
  • Cheng H, Fu CL. An iteration regularization for a time-fractional inverse diffusion problem. Appl Math Model. 2012;36:5642–5649. doi: 10.1016/j.apm.2012.01.016
  • Xiong X, Guo H, Liu X. An inverse problem for a fractional diffusion equation. J Comput Appl Math. 2012;236:4474–4484. doi: 10.1016/j.cam.2012.04.019
  • Nguyen HT, Le DL, Nguyen VT. Regularized solution of an inverse source problem for a time fractional diffusion equation. Appl Math Model. 2016;40:8244–8264. doi: 10.1016/j.apm.2016.04.009
  • Wang F, Hua Q, Liu CS. Boundary function method for inverse geometry problem in two-dimensional anisotropic heat conduction equation. Appl Math Lett. 2018;84:130–136. doi: 10.1016/j.aml.2018.05.004
  • Dehghan M, Yousefi SA, Rashedi K. Ritz-Galerkin method for solving an inverse heat conduction problem with a nonlinear source term via Bernstein multi-scaling functions and cubic B-spline functions. Inverse Probl Sci Eng. 2013;1:500–523. doi: 10.1080/17415977.2012.701627
  • Rad JA, Kazem S, Shaban M, et al. A new operational matrix based on Bernoulli polynomials, arXiv preprint arXiv, 2014, 1408.2207.
  • Kazem S. An integral operational matrix based on Jacobi polynomials for solving fractional-order differential equations. Appl Math Model. 2013;37:1126–1136. doi: 10.1016/j.apm.2012.03.033
  • Kazem S, Shaban M, Rad JA. Solution of the coupled Burgers equation based on operational matrices of d-dimensional orthogonal functions. Z Naturforsch . 2012;67:267–274. doi: 10.5560/zna.2012-0026
  • Dehghan M. Parameter determination in a partial differential equation from the overspecified data. Math Comput Model. 2005;41:196–213. doi: 10.1016/j.mcm.2004.07.010
  • Abbasbandy S, Kazem S, Alhuthali MS, et al. Application of the operational matrix of fractional-order legendre functions for solving the time-fractional convection-diffusion equation. Appl Math Comput. 2015;266:31–40.
  • Podlubony I. Fractional differential equations. San Diego (CA): Academic Press; 1999.
  • Povstenko Y. Linear fractional diffusion-wave equation for scientists and engineers. New York (NY): Birkhäuser; 2015.
  • Olver FW, Lozier DW, Boisvert RF, eds, et al. NIST handbook of mathematical functions hardback and CD-ROM. Cambridge: Cambridge University Press; 2010.
  • Kreyszig E. Introductory functional analysis with applications. New York: Wiley; 2007.
  • Rivlin TJ. An introduction to the approximation of functions. New York: Dover Publications; 1981.
  • Golbabai A, Beik SP. An efficient method based on operational matrices of Bernoulli polynomials for solving matrix differential equations. Comput Appl Math. 2015;34:159–175. doi: 10.1007/s40314-013-0110-y
  • Keshavarz E, Ordokhani Y, Razzaghi M. A numerical solution for fractional optimal control problems via Bernoulli polynomials. J Vib Control. 2016;22:3889–3903. doi: 10.1177/1077546314567181
  • Dehghan M, Shakeri F. Method of lines solutions of the parabolic inverse problem with an overspecification at a point. Numer Algorithms. 2009;50:417–437. doi: 10.1007/s11075-008-9234-3

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