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Main program: Chebfun SVD

svdfr.m  —  Compute singular value decomposition of the frequency response operator using integral formulation
all Matlab files  —  Zip file containing all Matlab files

Examples

FR_RD.m  —  Reaction-diffusion equation with Neumann boundary conditions
FR_OS_kz0.m  —  Orr-Sommerfeld equation
FR_LNS_kx0.m  —  Streamwise-constant linearized Navier-Stokes equations
FR_SOB_kz0.m  —  2D Stokes flow of Oldroyd-B viscoelastic fluids
FR_beam.m  —  Euler-Bernoulli beam with boundary actuation

Additional programs: integral formulation of differential equations

intbvp.m  —  Solve a scalar differential equation using integral formulation
intbvp_system.m  —  Solve a system of differential equations using integral formulation
 

This work utilizes Chebfun V4.2.2889, released in April 2013.
Chebfun is available at http://www.maths.ox.ac.uk/chebfun/

Citation

If you are using this software in your research or teaching, please include explicit mention of our paper and Chebfun.

@article{liejovJCP13,
   author  = {B. K. Lieu and M. R. Jovanovi{\'c}},
   title   = {Computation of frequency responses for linear time-invariant {PDE}s on a compact interval},
   journal = {J. Comput. Phys.},
   month   = {October},
   volume  = {250},
   pages   = {246-269},
   year    = {2013}
}

@misc{chebfunv4,
   author       = {Lloyd. N. Trefethen and Nicholas Hale and Rodrigo B. Platte and Tobin. A. Driscoll and Ricardo Pach{\'o}n},
   title        = {Chebfun Version 4},
   year         = {2013},
   note         = {http://www.maths.ox.ac.uk/chebfun/},
   howpublished = {University of Oxford}
}

If you are using intbvp.m please also cite

@article{dri10,
   author  = {T. A. Driscoll},
   title   = {Automatic spectral collocation for integral, integro-differential, and integrally reformulated differential equations},
   journal = {J. Comput. Phys.},
   volume  = {229},
   pages   = {5980-5998},
   year    = {2010}
}