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On the Applicability of an Isochronous Integration Framework for Parabolic/Hyperbolic Heat Conduction Type Problems

We demonstrate the applicability of a new isochronous integration (iIntegration) computational framework for the analysis of transient first/second-order systems via the new generalized single step single solve (GS4) family of algorithms, capable of simultaneously being applied to first- and second-order systems in time while providing attractive numerical and order-preserving attributes to capture the problem physics. To illustrate, we consider a recently developed model of heat conduction that was proposed to govern thermal transport from nano- to macro-scales, and is known in the literature as the C- and F-processes heat conduction model. This model inherits unique features and can represent either first- or second-order parabolic/hyperbolic heat conduction governing equations. A derivation of the model is first summarized, followed by the numerical discretization procedure and illustrative examples demonstrating the practicality and convenience of the new unified approach for modeling and analysis.