[Nonlinear_cover]

Nonlinear Analysis in Chemical Engineering

by Bruce A. Finlayson

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Programs that are available in either FORTRAN and/or MATLAB. The red color indicates they are available in both languages.

Programs in FORTRAN (download as nonlinear_prog.txt.)

Solve linear equations
invert.f ­ solves linear equations for dense, block tridiagonal, and tridiagonal matrices
invr.f ­ computes the inverse of a dense matrix
decomp.f ­ LU decomposition of a dense matrix
solve.f ­ solves for the right-hand side after an LU decomposition of a dense matrix
ludecom.f ­LU decomposition of a block tridiagonal matrix
fas.f ­ solves for the right-hand side after an LU decomposition of a block tridiagonalmatrix
invtri.f ­LU decomposition of a tridiagonal matrix
sweep.f ­ solves for the right-hand side after an LU decomposition of a tridiagonal matrix

Collocation matrices
coll.f ­ collocation matrices for problems with symmetry, planar, cylindrical, and spherical
planar.f ­ collocation matices for problems with no special symmetry

Applications ­ reaction/diffusion problems
ocrxn.f ­ solved using orthogonal collocation
ocferxn.f ­ solved using orthogonal collocation on finite elements
fdrxn.f ­ solved using the finite difference method

ivrxn.f ­ solved using an initial value method
pde.f ­ unsteady diffusion problem

ODE Solvers (download individually)
lsode.txt ­ Gear methods
rkf45.txt ­ 4th-5th order Runge-Kutta methods

Programs in MATLAB

Solve linear equations (Can download as linear_group.txt.)
OCFElud.m ­LU decomposition of a block tridiagonal matrix
OCFEfas.m ­ solves for the right-hand side after an LU decomposition of a block tridiagonalmatrix
lu_tri.m ­LU decomposition of a tridiagonal matrix
fas_tri.m ­ solves for the right-hand side after an LU decomposition of a tridiagonal matrix

Collocation matrices (Can download as collocation_group.txt.)
coll.m ­ collocation matrices for problems with symmetry, planar, cylindrical, and spherical
planar.m ­ collocation matices for problems with no special symmetry
coll_interp.m ­ interpolates between collocation points to give complete symmetric polynomial
planar_interp.m ­ interpolates between collocation points to give complete polynomial

Applications ­ reaction/diffusion problems (download individually, text files include all subroutines needed to run using MATLAB)
rxnOC.txt ­ solved using orthogonal collocation
rxnOCFE.txt ­ solved using orthogonal collocation on finite elements
rxnFD.txt ­ solved using the finite difference method

OC_unsteady.txt ­ unsteady diffusion problem

Applications ­ moving front problem
Mac_Langmuir.txt ­ MacCormack method with flux correction for transient adsorption (equilibrium) with a Langmuir isotherm

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