Modified Euler's Method (or RK2)

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SUMMARY

The discussion focuses on applying the Modified Euler's Method (RK2) to solve a differential equation representing the downward acceleration of a skydiver. The equation given is dv/dt = 32 - 0.005v^2, with a specified step size (h) of 0.5 seconds. Participants emphasize the importance of demonstrating initial work before receiving assistance, reinforcing the educational aspect of the forum. The goal is to approximate the skydiver's speed after 2 seconds using this numerical method.

PREREQUISITES
  • Understanding of differential equations and their applications
  • Familiarity with the Modified Euler's Method (RK2) for numerical solutions
  • Basic knowledge of calculus, particularly derivatives and integrals
  • Proficiency in using numerical methods for approximation
NEXT STEPS
  • Study the implementation of the Modified Euler's Method in Python or MATLAB
  • Explore the concept of numerical stability in differential equations
  • Learn about other numerical methods such as Runge-Kutta 4th Order
  • Practice solving similar differential equations with varying parameters
USEFUL FOR

This discussion is beneficial for students preparing for exams in calculus or numerical methods, educators teaching differential equations, and anyone interested in applying numerical techniques to real-world problems in physics and engineering.

kris
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I wondered if someone could do this for me so that i can use it as an example to learn from, it is from a past paper for an exam i will be sitting soon.

Suppose that a sky diver steps out of an aeroplane at an altitude of 10,000ft and that his downward acceleration is given by:

dv/dt = 32 - 0.005v^2

Use the modified Euler Method's with step size (h) of 0.5s to approximate the speed after 2s.

I vaguely understand it but exactly how to do it evades me.

Any help would be appreciated! :smile:
 
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