Approximation‎ ‎of a Leading‎ ‎Coefficient in an Inverse Heat Conduction Problem via the Ritz Method - Maryam Ghorbani; Kamal Rashedi (Mathematics Interdisciplinary Research, 2025)
‎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.