Numerical Recipes Forum  

Go Back   Numerical Recipes Forum > Obsolete Editions Forum > Methods: Chapters 16 and 17

Reply
 
Thread Tools Display Modes
  #1  
Old 08-18-2011, 07:48 PM
xapiens xapiens is offline
Registered User
 
Join Date: Aug 2011
Posts: 1
differential eq with square root

Hi!

I have to solve a system of two coupled nonlinear ordinary differential equations. In the function that defines the system there are terms with square root of the dependant variables. I tried to solve the system numerically but in the nmerical solution I get violent oscillations. Then I realized that the same problem appears in the numerical solution of this very simple exactly solvable differential equation: x'(t)=(1-x(t))^(1/2) with initial condition x(2.1)=0.9975. The exact solution is x(t)=(1/4)(4t-t^2).

It seems to me that the problem is the square root (1-x(t))^(1/2). When the numerical solution approach an extremum, then x'(t) and (1-x(t))^(1/2) both approach zero. But then (1-x(t)) also approaches zero, and in fact (1-x(t)) takes negative values, that makes the square root imaginary.

I explore the situation with the fourth-order Runge-Kutta method with step h=0.2 and in the firt iteration I find the complex value:

x(2.1)=1.00463+ 0.0042963 I

The same happens with the Euler method and the MidPoint Method

Any hint of how to get the correct numerical solution of this equation???

Thanks a lot!
Reply With Quote
Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is Off
HTML code is Off

Forum Jump


All times are GMT -5. The time now is 05:59 PM.


Powered by vBulletin® Version 3.8.6
Copyright ©2000 - 2014, Jelsoft Enterprises Ltd.