University of Kashan Mathematics Interdisciplinary Research 2538-3639 10 2 2025 06 01 Approximation‎ ‎of a Leading‎ ‎Coefficient in an Inverse Heat Conduction Problem via the Ritz Method 159 182 114910 10.22052/mir.2025.256068.1492 EN Maryam Ghorbani ‎Department of Mathematics, ‎University of Scince and Technology of Mazandaran, ‎Behshahr‎, ‎Iran Kamal Rashedi ‎Department of Mathematics, ‎University of Scince and Technology of Mazandaran, ‎Behshahr‎, ‎Iran Journal Article 2024 12 28 ‎This paper presents a numerical approach for reconstructing the leading coefficient in an inverse heat conduction problem (IHCP)‎. ‎We consider a one-dimensional heat equation with known input data‎, ‎including the initial condition‎, ‎a supplementary temperature measurement at the final time‎, ‎and two integral observations‎. ‎By incorporating the terminal condition‎, ‎the unknown spatially dependent coefficient is eliminated‎, ‎reducing the problem to a nonclassical parabolic equation‎. ‎The unknown temperature distribution and its derivatives are approximated and applied to the modified governing equation‎, ‎which is then discretized using operational matrices of differentiation‎. ‎To ensure stable derivative estimation‎, ‎the method is coupled with a regularization technique‎. ‎A least squares scheme is employed to formulate a nonlinear system of algebraic equations‎, ‎which is solved using Newton’s method‎. ‎The reliability of the proposed solution is demonstrated through several numerical examples‎. https://mir.kashanu.ac.ir/article_114910_55ba5850d43fcadb991c9eaeb8ad7d2b.pdf