Download NÜM 202 LINEAR ALGEBRA AND NUMERICAL METHODS

Anadolu University, Environmental Engineering Department
NUM 202 LINEAR ALGEBRA AND NUMERICAL METHODS
HOMEWORK 3 (2015-2016 Spring Semester)
1). Solve the following differential equation at x = 1.5 with the Euler method in one step. Find the true percent
error.
𝑑𝑦
= 3.2𝑥 4 − 4.1𝑥 2 + 6.8𝑥 − 5.2
𝑑𝑥
𝑦(1) = 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
− 3sin(𝑥) 𝑦 = 𝑥 2
𝑑𝑥
𝑦(𝜋/4) = 0
Solve it at x=π/2 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. The plate is heated at the edges as shown.
a)
Find the temperatures at the 5 nodes inside the plate (shown with
dark circles). Solve the linear algebraic equations using Gaussian elimination
with backsubstitution.
b)
Calculate the heat flux at the nodes. Each small square is 10 cm x 10
cm and the coefficient of thermal conductivity is 0.4 cal/s.cm.°C
Due : May 18, 2016 12:00 (Hand in to me at the Environmental Engineering Dept.)
The answers will be posted at 14:00 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