
Differential Equations Ordinary and Partial Differential Equations Math Forum 
 LinkBack  Thread Tools  Display Modes 
March 31st, 2015, 11:30 PM  #1 
Member Joined: Apr 2014 From: australia Posts: 68 Thanks: 32  Eulers Method
hello, need some guidance with this question: Consider the initial value problem; dy/dt = (cosy + 3) / y, y(0)=0.5 a) Use Euler's method with 5 steps to estimate y(0.1) up to three decimal points. Answer: I am confident with this part; y1= 0.655 y2 = 0.771 y3 = 0.867 y4 = 0.951 y5 = 1.027 b) Sketch the direction field in the domain 0 ≤ t ≤ 0.1, 0.2 ≤ y ≤ 1.4. ? c) Determine whether the approximate solution overestimates or underestimates the exact solution. ?? Any help would be appreciated. 
April 1st, 2015, 07:51 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,094 Thanks: 2360 Math Focus: Mainly analysis and algebra 
For the direction field, you pick pairs $(x,y)$ and at each point mark the gradient of the function. You can then sketch some solutions by following where the gradients lead. For the last part I think you should look at the solutions you sketched above. 

Tags 
eulers, method 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
matlab eulers method 2nd ode  sanam123  Calculus  0  February 12th, 2014 04:28 AM 
eulers constant  mathbalarka  Number Theory  15  May 30th, 2012 11:20 PM 
Solving Eulers Method  ferret  Applied Math  0  November 1st, 2011 08:15 PM 
which method....  eric3353  Calculus  3  July 3rd, 2008 03:23 PM 
What is the method?  guru123  Algebra  2  December 31st, 1969 04:00 PM 