Runge kutta method, Mathematics

As noted, Euler's method is little used in practice, as there are much better ways of solving initial value problems. By better, we mean, "able to achieve a result of the same precision using a larger step size". [Euler's method is also unstable for some problems where the step size can take you outside the physical domain of the function and the solution runs away to infinity.]

To improve on Euler's method, we will use the fourth-order Runge-Kutta method. This method requires four evaluations of the differential at each step, but often allows a much larger step size to achieve the same result. The method can be summarised as:

2432_Runge-Kutta method.png

where we have written h in place of the step size Δx.

  • Write a program to use the Runge-Kutta method of Eq. to solve the equation of motion of the projectile given in Eq.
  • Repeat your analysis of the step size required to achieve a given accuracy in the result. Doyou see an improvement? By how much?
Posted Date: 2/21/2013 4:46:12 AM | Location : United States







Related Discussions:- Runge kutta method, Assignment Help, Ask Question on Runge kutta method, Get Answer, Expert's Help, Runge kutta method Discussions

Write discussion on Runge kutta method
Your posts are moderated
Related Questions
Manuel is a cross-country runner for his school’s team. He jogged along the perimeter of a rectangular field at his school. The track is a rectangle that has a length that is 3 tim

The base of a right cylinder is the circle in the xy -plane with centre O and radius 3 units. A wedge is obtained by cutting this cylinder with the plane through the y -axis in

A standard deck of cards contains 52 cards. One card is selected at random. Determine a)    The probability that the card is a 8 or an Ace? b)    The probability that the card is

Sales price of a compact disc player is $200, each new cd is on sale for $12. kyle purchases a player and some cds for $224. how many cds were purchased?

Division of complex number Now, we gave this formula a long with the comment that it will be convenient while it came to dividing complex numbers so let's look at a couple of e

on which date of the week does 4th december 2001 falls?

In the shape of a cone a tank of water is leaking water at a constant rate of 2 ft 3 /hour .  The base radius of the tank is equal to 5 ft and the height of the tank is 14 ft.

without a calculator give the exact value of each of the following logarithms. (a) (b) log1000 (c) log 16 16 (d) log 23 1  (e)  Solution (b) log10

Find out the domain of each of the following.  (a) f (x,y) = √ (x+y) (b) f (x,y) = √x+√y  (c) f (x,y) = ln (9 - x 2 - 9y 2 ) Solution (a) In this example we know