Original comment by Benjamin Brown (Bitbucket: Benjamin Brown).

• set attachment to "1d_burgers_equation_chebyshev.png"

Burgers equation is now implemented in both Fourier and Chebyshev domains.

Early results look good; we're able to at least qualitatively match [see attached figure] fig 18 from Ascher et al. (1995). This test was done with nu=0.01, dt=1e-2, and nx=64. These are different choices than Ascher et al., except nu.

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Original comment by J. S. Oishi (Bitbucket: jsoishi).

Nice work, @bpbrown ! But could you give a more complete reference for Ascher et al. (1995)?

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Original comment by Benjamin Brown (Bitbucket: Benjamin Brown).

A library of nice IMEX and related timestepping methods

Generating IMEX schemes up to 4th order, plus tests of stability

Ascher, U. M., Ruuth, S. J., & Wetton, B. T. (1995). Implicit-explicit methods for time-dependent partial differential equations. SIAM Journal on Numerical Analysis, 32(3), 797-823.

http://epubs.siam.org/doi/abs/10.1137/0732037

Generalizing same IMEX schemes of Ascher et al 1995 to variable step size

Wang, D., & Ruuth, S. J. (2008). Variable step-size implicit-explicit linear multistep methods for time-dependent partial differential equations. Journal of Computational Mathematics, 26(6), 838-855.

http://www.global-sci.org/jcm/volumes/v26n6/pdf/266-838.pdf

Runge-Kutta implicit-explicit methods

Ascher, U. M., Ruuth, S. J., & Spiteri, R. J. (1997). Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations. Applied Numerical Mathematics, 25(2), 151-167.

http://www.sciencedirect.com/science/article/pii/S0168927497000561

Study of several 4th order methods for PDEs (constant step size only)

Kassam, A. K., & Trefethen, L. N. (2005). Fourth-order time-stepping for stiff PDEs. SIAM Journal on Scientific Computing, 26(4), 1214-1233.

http://epubs.siam.org/doi/abs/10.1137/S1064827502410633

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