Anadolu University, Environmental Engineering Department
NUM 202 LINEAR ALGEBRA AND NUMERICAL METHODS
HOMEWORK 3 (2015-2016 Fall Semester)
1). Solve the following differential equation at x = 0.5 with the Euler method in one step. Find the true percent
error.
𝑑𝑦
= 3.2𝑥 3 + 4.1𝑥 2 − 6.8𝑥 − 5.2
𝑑𝑥
𝑦(0) = 4.2
2). Solve the differential equation in Q1 with the Euler method with a step size of 0.05. Find the true percent
error.
3). Solve the differential equation in Q1 with the Classical Runge-Kutta method in one step.
4). The following differential equation is given
𝑑𝑦
+ 2sin(𝑥) 𝑦 = 𝑥 2
𝑑𝑥
𝑦(0) = 0.4
Solve it at x=1 with the Classical Runge-Kutta method.
5). The following differential equation is given
𝑑𝑦
𝑑𝑥
− 2𝑒 𝑦 = −4√𝑥
𝑦(1) = −1.2
Solve it at x = 2 with the classical Runge-Kutta method in two steps.
6). The following thin metal plate is given
40 40
320
°°C
90
20
20
The plate is heated at the edges as shown.
a)
Find the temperatures at the 4 nodes inside the plate. Solve the linear algebraic equations using
Gaussian elimination with backsubstitution.
b) Calculate the heat flux at the upper-right node . The distance between the nodes is 12 cm and the
coefficient of thermal conductivity is 0.4 cal/s.cm.°C
c) What type of matrix is the coefficient matrix in this question
In this example, you will also need the temperatures at the corners which are equal to the temperatures at the
edges leading to them. Label the temperatures only with one subscript (i.e. T1) and begin at the leftmost one.
Due : January 7, 2016 16:00 (Hand in to me at the Environmental Engineering Dept.)
The answers will be posted at 16:00 on the website.
Homework format:

Head page (Name of course, Homework No., Student name, number, Name of lecturer, Due date, Signature)

Questions and solution written by hand (readable and understandable, defining each step)
Your signature tells that you have completed this homework by your own effort. Use only white A4 paper.
50% reduction in grade will be done for homeworks not following this format.
Late homeworks will not be accepted. Attach the papers together with a staple.
Prof. Dr. Erdem Ahmet Albek