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Math 151B Homework #3: Stability Analysis of Explicit and Implicit Euler Methods, Assignments of Mathematics

University of California - Los Angeles (UCLA)Mathematics

Instructions for homework #3 in math 151b, focusing on stability analysis of explicit and implicit euler methods. Students are required to find the region of absolute stability for each method, and make predictions about the behavior of the methods for different step sizes (h = 0.5, 1.5, 2.1). They are also asked to confirm their findings numerically or graphically.

Typology: Assignments

Pre 2010

Uploaded on 08/30/2009

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koofers-user-vum 🇺🇸

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Math 151B Homework #3 – due Friday 1/30, in class
1. stability
Consider the intial value problem
y0=−y+1
t,1≤t≤100, y(1) = 1
a. Find the region of absolute stability for explicit Euler’s method.
b. What do you expect to happen when h= 0.5?
c. What do you expect to happen when h= 1.5?
d. What do you expect to happen when h= 2.1?
e. Confirm the above numerically/graphically.
2. implicit Euler
Repeat the first problem, using implicit Euler’s method.

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Math 151B Homework #3 – due Friday 1/30, in class

  1. stability Consider the intial value problem y′^ = −y +

t , 1 ≤ t ≤ 100 , y(1) = 1 a. Find the region of absolute stability for explicit Euler’s method. b. What do you expect to happen when h = 0.5? c. What do you expect to happen when h = 1.5? d. What do you expect to happen when h = 2.1? e. Confirm the above numerically/graphically.

  1. implicit Euler Repeat the first problem, using implicit Euler’s method.