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An alternative discretization and solution procedure for the dual phase-lag equation. (English) Zbl 1105.65094

Summary: We describe an alternative numerical treatment of the dual phase-lag equation often used to account for microscale, short-time heat transport. The approach consists of an undecomposed formulation of the partial differential equation resulting from Taylor expansion with respect to lag times of the original delay partial differential equation. Trapezoidal integration in time and centered differencing in space provide an accurate discretization, as demonstrated by comparisons with analytical and experimental results in one dimension, and via grid-function convergence tests in three dimensions. For relatively fine 3D grids the approach is approximately six times faster than a standard explicit scheme and nearly three times faster than an implicit method employing conjugate gradient iteration at each time step.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35R10 Partial functional-differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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