Spring 2006

Courtesy of Richard J. Braun

Matlab examples codes.

Warming up

Plot1.m

Plot2.m

Plot3.m

Plotseq3.m Sequence of plots with increasing resolution

RatFunPlot.m Basic plot of rational function approximation and exp(-x)

RatFunPlot2.m Fancier plot of rational function approximation and exp(-x)

Table1.m Table example from handout

TableProb.m Table problem in homework

Format_ex.m Examples of different formats

TestSign.m TestSign2.m Examples if-else-end constructs Darts.m Estimating Pi (From Van Loan)

Zoom.m Small scale look at function (from Van Loan)

Zoom2.m Small scale look at function, modified

Quadratic formula Quad1.m Quad2.m

Numdiff.m Numerical differentiation, centered formula

Functions

MyExpF.m MyExp1.m MyExp2.m Functions for Taylor polynomials approximating the exponential from Van Loan

TestMyExpRB.m TestMyExpRB1.m TestMyExpRB2.m Scripts for testing above functions (updated Van Loan)

trap1_05f.m Use this trapezoidal rule code as a starting point for Hw 6.

Functions

Bisection1.m Bisection method, no Matlab functions (yuck)

Bisection2.m Bisection method, with Matlab functions

Bisection3.m Bisection method as a Matlab function (black box for answer)

Sample function file f1.m

f2.m Simple function to zero, f(x)=x^3-x^2

f2p.m Derivative of f2.m

SimpleNewton.m Very simple implementation of Newton method

Ordofconv.m Two sequences with different order of convergence

RJB_Newton2.m Implementation of Newton method

RJB_Secant2.m Implementation of Secant method

Direct Solution of Linear Systems

GE06.mSimplistic implementation of Gaussian Elimination (script)

GEBS04_1.m Simplistic implementation of Gaussian Elimination and Backward Substitution (script)

GEBS04.m Function version of GEBS04_1.m

GEPPBS04_1.m Script, added partial pivoting GEPPBS04.m Function version

Benchmarking: TimeGEandBS.m Script for timings (calls GEBS04.m and UTriSolAug.m).

UTriSolAug.m Function, augmented matrix form of Backward Substitution.

Iterative Solution of Linear Systems

GaussJac.m Large system trends, Jacobi iteration

GaussSeid.m Large system trends, Seidel iteration

Splines and such

Home-grown splines: SplineClampUni.m Clamped ends; SplineNatUni.m Natural splines.

Matlab spline function: SplineMat.m (based on Van Loan)

Numerical Integration

Simple Composite Trapezoidal rule: easiest: Trapez.m vectorized: Trap2.m

Simple Composite Simpson's rule: easiest: Simp1.m vectorized: Simp2.m

Initial Value Problems

Euler1Eq.m solves single ode

RK4Sys_ex.m solves harmonic oscillator with RK4 method

ode_ex.m solves harmonic oscillator: harm_osc.m

Linear or Nonlinear Boundary Value Problems

bvp_ex.m Script for using bvp4c in matlab. Functions needed: bvp_exf.m bvp_exbc.m

PDE examples

heateq_explicit.m Explicit or Forward Difference method for heat equation.

heateq_bkwd.m Fully implicit or Backward Difference method for heat equation.

heateq_bkwd.m Crank-Nicolson method for heat equation.

PoissonEqEx.m Finite difference method for a Poisson equation.

Department of Mathematical Sciences