Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  investigates the inverse problems of simultaneous reconstruction of time-dependent thermal conductivity, convection or absorption coefficients in the parabolic heat equation governing transient heat and bio-heat thermal processes. Using initial and boundary conditions, as ll as heat moments as over-determination conditions ensure that these inverse problems have a unique solution. Hover, the problems are still ill-posed since small errors in the input data cause large errors in the output solution. To overcome this instability  employ the Tikhonov regularization. A discussion of the choice of multiple regularization parameters is provided. The finite-difference method with the Crank–Nicolson scheme is employed as a direct solver. The resulting inverse problems are recast as nonlinear minimization problems and are solved using the lsqnonlin routine from the MATLAB toolbox. Numerical results are presented and discussed.
['Mj Huntul', 'D. Lesnic', 'M. S. Hussein']
I am writing a research paper on a idea Reconstruction of time-dependent coefficients from heat moments
[{"from": "human", "value": "I am writing a research paper on a idea Reconstruction of time-dependent coefficients from heat moments"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  investigates the inverse problems of simultaneous reconstruction of time-dependent thermal conductivity, convection or absorption coefficients in the parabolic heat equation governing transient heat and bio-heat thermal processes. Using initial and boundary conditions, as ll as heat moments as over-determination conditions ensure that these inverse problems have a unique solution. Hover, the problems are still ill-posed since small errors in the input data cause large errors in the output solution. To overcome this instability  employ the Tikhonov regularization. A discussion of the choice of multiple regularization parameters is provided. The finite-difference method with the Crank\u2013Nicolson scheme is employed as a direct solver. The resulting inverse problems are recast as nonlinear minimization problems and are solved using the lsqnonlin routine from the MATLAB toolbox. Numerical results are presented and discussed."}]