Numerical approach for reconstructing an unknown source function in inverse parabolic problem

Document Type : Research Paper


1 Department of Mathematics, Semnan University, Semnan, Iran

2 Department of Mathematics, Semnan University, Semnan, Iran.


‎The inverse problem considered in this paper is devoted to reconstruction of the unknown source term in parabolic equation from additional information which is given by measurements at final time‎. ‎The cost functional is introduced and existence of the minimizer for this functional is established‎. ‎The numerical algorithm to solve the inverse problem is based on the Ritz-Galerkin method with shifted Legendre polynomials as basis functions‎. ‎Finally‎, ‎some numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for test example‎.


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Volume 12, Issue 1
May 2021
Pages 555-565
  • Receive Date: 01 May 2018
  • Revise Date: 13 June 2018
  • Accept Date: 16 April 2019