A Numerical Method for the Hyperbolic-heat Conduction Equation Based on Multiple Scale Technique Suman Roy * A. S. Vasudeva Murthy † Ramesh B. Kudenatti ‡ Abstract For weakly hyperbolic heat equation a numerical scheme based on multiple scale technique is derived. The advantages over the conventional finite difference method are highlighted. Keywords: Heat Conduction Equation; Weakly Hyperbolic Equation; Multiscale Techniques; Fourier Series; Stability analysis. 1 Introduction Heat waves in a conducting domain are generated by initial, boundary and source disturbances, and are governed in the short time scales by the hyperbolic heat conduction equation. We consider one- dimensional wave equation for heat conduction in a thin, homogeneous, finite rod of constant cross- sectional area. The following discussion is borrowed from [7] ( see also [10]). Assuming that the rod has a constant thermal diffusivity, κ> 0, that occupies the open interval (0,l) along the χ-axis of a Cartesian coordinate system, heat conduction within the rod is governed by the so called Maxwells-Cattaneo law, leading to the initial boundary value problem (IBVP) ∂ τ θ(χ, τ )+ λ 0 ∂ 2 τ θ(χ, τ )= κ∂ 2 χ θ(χ, τ ), (χ, τ ) ∈ (0,l) × (0, ∞), (1a) θ(0,τ )=0,θ(l, τ )=0,τ> 0, (1b) θ(χ, 0) = θ 0 g(χ/l),∂ τ θ(χ, 0) = 0,χ ∈ (0,l), (1c) * SETLABS, Infosys Technologies Ltd., No.44 Electronics City, Hosur Road, Bangalore- 560 100, India, e-mail: suman roy@infosys.com † Corresponding author, TIFR- Center for Applicable Mathematics, Yelahanka New Town, Bangalore-560 065, e-mail: vasu@math.tifrbng.res.in ‡ TIFR- Center for Applicable Mathematics, Yelahanka New Town, Bangalore-560 065, e-mail: ramesh@bub.ernet.in 1