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The objective of this article is to introduce a novel technique for computingnumerical solutions to the nonlinear inverse heat conduction problem. Thisinvolves solving nonlinear parabolic equations with Cauchy data provided on oneside $\Gamma$ of the boundary of the computational domain $\Omega$. The keystep of our proposed method is the truncation of the Fourier series of thesolution to the governing equation. The truncation technique enables us toderive a system of 1D ordinary differential equations. Then, we employ thewell-known Runge-Kutta method to solve this system, which aids in addressingthe nonlinearity and the lack of data on $\partial \Omega \setmunus \Gamma$.This new approach is called the dimensional reduction method. By converting thehigh-dimensional problem into a 1D problem, we achieve exceptionalcomputational speed. Numerical results are provided to support theeffectiveness of our approach.

The dimensional reduction method for solving a nonlinear inverse heat conduction problem with limited boundary data