The application of Runge–Kutta schemes designed to enjoy a large region of absolute stability can significantly increase the efficiency of numerical methods for PDEs based on a method of lines approach. In this work we investigate the improvement in the efficiency of the time integration of relaxation schemes for degenerate diffusion problems, using SSP Runge–Kutta schemes and computing the maximal CFL coefficients. This technique can be extended to other PDEs, linear and nonlinear, provided the space operator has eigenvalues with a nonzero real part.
Cavalli, F., Naldi, G., Puppo, G., Semplice, M., Increasing Efficiency Through Optimal RK Time Integration of Diffusion Equations, Contributed paper, in Hyperbolic Problems: Theory, Numerics, Applications, (Lyon, 17-21 July 2006), Springer Berlin Heidelberg, Berlin Heidelberg 2008: 955-962. 10.1007/978-3-540-75712-2_100 [http://hdl.handle.net/10807/85649]
Increasing Efficiency Through Optimal RK Time Integration of Diffusion Equations
Cavalli, FaustoPrimo
;
2008
Abstract
The application of Runge–Kutta schemes designed to enjoy a large region of absolute stability can significantly increase the efficiency of numerical methods for PDEs based on a method of lines approach. In this work we investigate the improvement in the efficiency of the time integration of relaxation schemes for degenerate diffusion problems, using SSP Runge–Kutta schemes and computing the maximal CFL coefficients. This technique can be extended to other PDEs, linear and nonlinear, provided the space operator has eigenvalues with a nonzero real part.
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