A spectral collocation approach based on shifted Viet Lucas polynomials for microscale heat transfer modeling in thin metal films

This study presents a concise and highly accurate spectral collocation technique (SCT) for simulating microscale heat transfer in thin metal films. The approach relies on shifted Vieta–Lucas polynomials (SVLPs), which provide useful mathematical features like orthogonality, symmetry and recurrence relations. These properties are used to derive operational matrices (OMs) that enable the numerical solution of heat transfer equations with complex spatial and temporal characteristics. For compatibility with the initial–boundary conditions (IBCs), specially tailored basis functions are utilized. The solution is approximated by a spectral expansion in space and time, and the governing partial differential equation (PDE) is reduced to a system of algebraic equations via collocation at carefully selected points. The convergence and stability of the method are confirmed through theoretical analysis. Numerical tests demonstrate its superior accuracy and efficiency compared with existing methods. The developed method provides a robust tool for simulating microscale heat transfer phenomena in modern engineering and physical applications.