Numerical Differential Equations
MA 512
Spring, 2017
M-Files
| Filename | Description |
| absStabRegionAdamsDemo.m |
Plots absolute-stability regions for Adams-Bashforth and Adams-Moulton methods of orders 1-6. |
| absStabRegionBDFdemo.m |
Plots absolute-stability regions for Backward Differentiation Formula (BDF) methods of orders 1-6. |
| absStabRegionRKdemo.m |
Plots absolute-stability
regions for explicit Runge-Kutta methods of orders 1-8. |
| abs_stab_region.m |
Draws the boundary of the absolute-stability region
of a method, given a
function g that characterizes the region by
abs(g(z))<1. |
| adi_pre.m |
Implements ADI
preconditioning. |
| biharmonic_op.m |
Creates a sparse matrix for
the 2D discrete biharmonic operator. |
| brusselatorfun.m |
Evaluates the right-hand side
of the Brusselator ODE. |
| brusselatorjac.m |
Evaluates the Jacobian with respect to y of the right-hand side of the Brusselator ODE. |
| condif.m |
Creates a sparse matrix for
the 2D convection-diffusion operator. |
| f_Bratu.m |
Evaluates the residual function for the
Bratu problem. |
| fpr_Bratu.m |
Evaluates the Jacobian of the residual
function for the Bratu problem. |
| forward_euler.m |
Implements the forward-Euler method. Used
by stiff_demo.m. |
| gaussseidel.m |
Implements the
Gauss-Seidel method. |
| gmres_demo.m |
Demonstrates the performance
of GMRES on the model 2D Poisson problem. Requires
adi_pre.m, condif.m, loadrhs.m, and rhsfun.m. |
| hw2funevent.m |
"Event" function for terminating
integration of the Homework 2 IVP. Used by ode45_demo.m. |
| it_method_demo.m |
Demonstrates the
performance of the classical iterative methods on the
model 2D Poisson problem. Requires gaussseidel.m,
jacobi.m, laplacian.m, loadrhs.m, rhsfun.m, and sor.m. |
| jacobi.m |
Implements
Jacobi iteration. |
| laplacian.m |
Creates a sparse
discrete 2D Laplacian matrix. |
| loadrhs.m |
Creates the
right-hand side vector for the discretized model Poisson
problem. |
| newton_bratu_demo.m |
Demonstrates Newton's method with
backtracking on the Bratu (Gelfand) problem. Requires
newtonbt.m, laplacian.m, loadrhs.m, rhsfun.m, and
seesol.m. |
| newtonbt.m |
Implements Newton's method with
backtracking. |
| ode45_demo.m |
Demonstrates MATLAB's ode45 on the HW2 IVP.
Requires hw2funevent.m. |
| oregonatorfun.m |
Evaluates the right-hand side of the Oregonator ODE. |
| oregonatorjac.m |
Evaluates the Jacobian with respect to y of the right-hand side of the Oregonator ODE. |
| oregonatormovie.m |
Creates and returns a movie
file for the Oregonator problem. |
| mol_demo_1D.m |
Demonstrates the performance
of the method of lines on an initial-boundary value
problem for the 1D heat equation. |
| pcg_demo.m |
Demonstrates the performance
of PCG on the model 2D Poisson problem. Requires
adi_pre.m, biharmonic.m, laplacian.m, loadrhs.m, and
rhsfun.m. |
| PhasePlaneQuiverPlots.m |
Shows phase-plane "quiver" plots for
selected ODEs in two dependent variables. |
| predcor2.m |
Implements a 2nd-order
predictor-corrector method. See the comments in the code
for more information. |
| rhsfun.m |
Evaluates a function on the mesh for the discretized 2D model Poisson problem. |
| seesol.m |
Used to visualize the solution surface of a
function of two variables on a square mesh. |
| sor_analyzer.m |
Plots the spectral radius of
the SOR iteration matrix for 0 < omega < 2. Requires
spec_rad.m. |
| sor.m |
Implements SOR. |
| spec_rad.m |
Computes the spectral radius.
|
| stiff_demo.m |
Demonstrates the forward Euler, backward
Euler, and MATLAB's ode45 on a stiff ODE from Gear's book.
Requires forward_euler.m. |