Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
A validated parallel across time and space solution of the heat transfer equation
Applied Numerical Mathematics
Parallel implementation of a high-order implicit collocation method for the heat equation
Mathematics and Computers in Simulation
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We combine a high-order compact finite difference scheme to approximate the spatial derivatives and collocation techniques for the time component to numerically solve the two-dimensional heat equation. We use two approaches to implement the time collocation methods. The first one is based on an explicit computation of the coefficients of polynomials and the second one relies on differential quadratures. We also implement a spatial collocation method where differential quadratures are utilized for spatial derivatives and an implicit scheme for marching in time. We compare all the three techniques by studying their merits and analyzing their numerical performance. Our experiments show that all of them achieve high-accurate approximate solution but the time collocation method with differential quadrature offers (with respect to the one with explicit polynomials) less computational complexity and a better efficiency. All our computations, based on parallel algorithms, are carried out on the CRAY SV1.