Numerical Methods

Example of MATLAB 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 of if-else statements

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

MATLAB codes for class

CHAPTER1

bisect.m (Bisection method from Sauer's book)

bisection.m (Bisection method revised)

exa_mybisect.m (Animation for bisection method)

fpi.m (Fixed Point Iterations from Sauer's book)

fpiseq.m (Fixed Point Iteration. Outputs the iteration sequence.)

exa_myfpi.m (Animation for fixed point iteration)

fixpt.m ( Another Fixed Point Iteration function with additional output)

newton.m (Newton's Method)

secant.m (Secant Method, with stopping criteria |x_old -x_new| < tol)

secant2.m (Secant Method with Max # of iterations as input argument)

CHAPTER2

GE.m Simplistic implementation of Gaussian Elimination (script)

backsub.m Book Implementation of back solve alhorithm

UTriSolAug.m Function, to solve an Upper triangular system by Backward Substitution.

trisys.m ( Gussian Elimination method for a tridiagonal system)

CHAPTER3

newtdd.m (Newton's Divided Differences Interpolant - from Sauer's book)

runge.m Function that shows the Runge phenomena for f(x) =1/(1 +12 x^2) on [-1 1].

CHAPTER4

DrugModel.m drug model for example 4.11, page 214 Sauer's book.

CHAPTER5

trapezoid.m Uses the composite trapezoidal rule to approximate Integrals

CTRuleOrder.m Script file to check that the Error for the Composite Trapezoid Rule is: Error(h) = O(h^2). The function: f (x)=sin(x) on [0 pi].

CHAPTER6

euler.m Euler's method for solving IVPs

exa_euler.m Example:y'= t*y +t^3; The exact soln:y=3*e^(t^2/2)-t^2-2;

heunT.m Heun's ( or trapezoid) method for solving IVPs

rk4.m Runge-Kutta of order 4 method for solving IVPs

rk4s.m Runge-Kutta of order 4 method for Systems

VF.m Matlab Vector Function - RHS for a system of DE to be solved by rk4s.m

RK4Sys_ex.m solves harmonic oscillator with RK4 method

ode_ex.m solves harmonic oscillator: harm_osc.m

CHAPTER7

VF4ivp.m Matlab Vector Function - RHS for an IVP system used with the shooting method

F4bis.m Matlab scalar function (to be used by bisection method) for solving a bvp using the shooting method

Sierpinski fun

sg.m

gasket.m

Lorenz System

lorenz.m

lrun.m

Department of Mathematical Sciences