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


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


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

   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}

   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         = {},
   howpublished = {University of Oxford}

If you are using intbvp.m please also cite

   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}