Date assigned: May 20, 2016
Date due: May 31, 2016
Numerical Methods
Homework 5
1) The differential equation dp/dt = kmax (1-p/pmax) p can be used to model a population. pmax
is a constant that equals the maximum population and kmax is a constant that equ

REGISTER OF SPONSORS (Tiers 2 & 5 and Sub Tiers Only)
DATE:
28-December-2016
Register of Sponsors Licensed Under the Points-based System
This is a list of organisations licensed to sponsor migrants under Tiers 2 & 5 of the Points-Based System. It shows th

S EC . 7.3
R ECURSIVE RULES AND ROMBERG I NTEGRATION
377
7.3 Recursive Rules and Romberg Integration
In this section we show how to compute Simpson approximations with a special linear
combination of trapezoidal rules. The approximation will have greater

Physics 115/242
Romberg Integration
Peter Young
In this handout we will see how, starting from the trapezium rule, we can obtain much more
accurate values for the integral by repeatedly eliminating the leading contribution to the error.
This is known as R

S EC . 6.1
A PPROXIMATING THE D ERIVATIVE
323
Central-Difference Formulas
If the function f (x) can be evaluated at values that lie to the left and right of x, then
the best two-point formula will involve abscissas that are chosen symmetrically on both
si

Jim Lambers
MAT 460/560
Fall Semeseter 2009-10
Lecture 29 Notes
These notes correspond to Section 4.5 in the text.
Romberg Integration
Richardson extrapolation is not only used to compute more accurate approximations of derivatives,
but is also used as th

Math 523: Numerical Analysis I
Solution of Homework 3. Numerical Quadrature
Problem 1. Consider the integral
with n panels.
R1
0
ex dx. We divide the interval [0, 1] into a uniform partition
(a) Apply the composite Trapezoid rule for n = 1, 2, 4, 8, 16, 3

Date assigned: April 14, 2016
Date due: April 21, 2016
MAT202E NUMERICAL METHODS
HOMEWORK 4
1) The following table has values for f(x). a) Integrate between x=1.0 and x=1.7 by using the
trapezoidal rule (h=0.1). b) Repeat the integration this time using a

Date assigned: March 22, 2016
Date due: April 4, 2016
Numerical Methods
Homework 3
1) Given the four points (1,2), (3,4), (5,3), (9,8), write the cubic in Lagrangian form that
passes through them. Multiply out each term to express in the standard form, as

Numerical ODE SOLUTIONS
Initial-Value Problems
Programming Euler Method
f=inline('1-2*v^2-t','t','v')
h=0.01
t=0
v=1
T(1)=t;
V(1)=v;
for i=1:100
v=v+h*f(t,v)
t=t+h;
T(i+1)=t;
V(i+1)=v;
end
dv
1 2v 2 t.
dt
v(0) 1
for ti 0.01i,
i 1,2,.,100
Definition of th

Chapter 7
Numerical Differentiation and
Numerical Integration
* 3/1/13 EC
Whats Ahead
A Case Study on Numerical Differentiation: Velocity Gradient for Blood Flow
Finite Difference Formulas and Errors
Interpolation-Based Formulas and Errors
Richardson