The present work aims at applying the ideas in the so-called Coupled Integral Equations Approach (CIEA) to the one-dimensional thermal wave propagation problem in a finite Solid medium, leading to improved lumped-differential formulations through Hermite-type Approximations for integrals. The application of CIEA methodology makes it possible to Reduce the partial differential equation governing the hyperbolic heat conduction problem To a simple system consisting of two or three ordinary differential equations for the average And surface temperatures, depending on the choice of the Hermite-type approximation.
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