Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 12 1 2021 05 01 Numerical approach for reconstructing an unknown source function in inverse parabolic problem 555 565 4838 10.22075/ijnaa.2021.4838 EN Javad Damirchi Department of Mathematics, Semnan University, Semnan, Iran Ali Janmohammadi Department of Mathematics, Semnan University, Semnan, Iran. Masoud Hasanpour Department of Mathematics, Semnan University, Semnan, Iran. Reza Memarbashi Department of Mathematics, Semnan University, Semnan, Iran. Journal Article 2018 05 01 ‎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. https://ijnaa.semnan.ac.ir/article_4838_2f9f68db09e1136e34bc21f572da10a6.pdf