approximation‎ ‎of a leading‎ ‎coefficient in an inverse heat conduction problem via the ritz method

‎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.