Matlab Programs

Matlab Programs for Math 5486

• numode.m - general-purpose numerical ordinary differential equation solver and grapher
• Euler method:  neuler.m    neulerf.m
• Improved Euler method:  ieuler.m    ieulerf.m
• Midpoint method:  midp.m    midpf.m
• Fourth Order Runge-Kutta:  rk4.m    rk4f.m
• Sample Differential Equations:
  • Scalar ode du/dt = (1 - 4t/3)u:   gv.m  Solution:  gvs.m
  • Undamped pendulum:   upend.m
  • Damped pendulum:   dpend.m
  • Van der Pol oscillator:   vpd.m
  • Predator-prey model:   pp.m

Matlab Programs for Math 5485

• rn.m - rounding function
• iter.m - function iteration
• secant.m - secant method
• newton.m - Newton's method
• gauss.m - regular Gaussian elimination
• gaussr.m - alternative regular Gaussian elimination
• back.m - back substitution
• trid.m - generate tridiagonal matrices
• specr.m - compute spectral radius of a matrix
• miter.m - matrix iteration
• jacobi.m - Jacobi iteration
• gs.m - Gauss-Seidel iteration
• sor.m - SOR iteration
• sorw.m - optimal SOR parameter
• sorad.m - compute SOR spectral radius
• newton3.m - solve z^3 = 1 by Newton's method
• robot.m - position robot arms by Newton's method
• lagrangep.m - Lagrange interpolating polynomial
• lagrangeplot.m - Plot Lagrange interpolating polynomial
• ix2.m - the function 1/(1+x^2)

Matlab Programs for Math 4457

• dspr.m - normal modes of oscillation of linear mass & spring system
• gspr.m - graph oscillations of linear mass & spring system
• cspr.m - show oscillations of linear mass & spring system
• mspr.m - show oscillations and normal components of linear mass & spring system
• dyst.m - dynamical modes of oscillation of 2D or 3D structure
• network.m - finds potentials and currents in electrical networks
• strut.m - graphs a structure in two or three dimensions, and determines its stability
• graph.m - finds incidence matrix and plots a graph
• quasi.m - plot quasi-periodic function (2 modes)
• quasi3.m - plot quasi-periodic function (3 modes)

Computational subroutines

• incidence.m - computes incidence matrix from edge matrix
• ngon.m - finds coordinates for unit polygon
• solids.m - edge matrices and vertices for regular solids
• house.m - edge matrices and vertices for houses
• tr3.m - linear transformations of multiple points

Graphics subroutines

• button.m - sets up buttons for interacting with dynamical graphics
• circle.m - draws circles
• triangle.m - draws triangles
• linevec.m - draws lines using vector coordinates
• arrowvec.m - draws directed lines using vector coordinates
• textvec.m - writes text at specified coordinates

• phase3.m - phase portrait of 3D ordinary differential equation
• heat.m - numerical solution of 1D heat equation (Crank-Nicholson method)
• wave.m - numerical solution of 1D wave equation (finite difference method)
• go2.m - graph solutions to planar linear o.d.e.'s
• go3.m - graph solutions to three-dimensional linear o.d.e.'s
• dspr.m - normal modes of oscillation of linear mass & spring system
• gspr.m - graph oscillations of linear mass & spring system
• cspr.m - show oscillations of linear mass & spring system
• mspr.m - show oscillations and normal components of linear mass & spring system
• dyst.m - dynamical modes of oscillation of 2D or 3D structure
• phase.m - phase portrait of 2D ordinary differential equation
• phaseg.m - phase portrait plus graph of second order ordinary differential equation
• phasem.m - phase portrait plus movie of pendulum motion

Computational subroutines

• o3.m - a simple 3D differential equation
• fset.m - set up for Fourier sine series
• fsine.m - plot Fourier sine series
• fset2.m - set up for Fourier series
• fouri.m - plot Fourier series
• lo2.m - general planar linear first order o.d.e.
• lo3.m - general three-dimensional linear first order o.d.e.
• button.m - sets up buttons for interacting with dynamical graphics
• quasi.m - plot quasi-periodic function (2 modes)
• quasi3.m - plot quasi-periodic function (3 modes)
• pendulum.m - nonlinear pendulum differential equations
• dpendulum.m - damped nonlinear pendulum differential equations
• fpendulum.m - forced nonlinear pendulum differential equations
• fdpendulum.m - forced damped nonlinear pendulum differential equations

• Qplot.m - for graphing quadratic functions
• ellipse.m - graphs ellipses and their principal axes
• ellipsoid.m - graphs ellipsoids and their principal axes
• network.m - finds potentials and currents in electrical networks
• strut.m - graphs a structure in two or three dimensions, and determines its stability
• graph.m - finds incidence matrix and plots a graph
• cgraph.m - finds incidence matrix and plots complete graph
• ograph.m - finds incidence matrix and plots circular graph

Computational subroutines

• incidence.m - computes incidence matrix from edge matrix
• cedge.m - finds edge matrix for complete graph
• oedge.m - finds edge matrix for circular graph
• cgon.m - finds edge matrix and vertex coordinates for complete graph
• ogon.m - finds edge matrix and vertex coordinates for circular graph
• ngon.m - finds coordinates for unit polygon
• solids.m - edge matrices and vertices for regular solids
• house.m - edge matrices and vertices for houses
• tr3.m - linear transformations of multiple points

Graphics subroutines

• circle.m - draws circles
• triangle.m - draws triangles
• linevec.m - draws lines using vector coordinates
• arrowvec.m - draws directed lines using vector coordinates
• textvec.m - writes text at specified coordinates

Phone: 612-624-5534
Fax: 612-626-2017
e-mail: olver@ima.umn.edu
http://www.math.umn.edu/~olver