Engineering analysis 2 - Speech or Presentation Example

This method, of course, introduces error due to the nature of the treatment that is given to the differential curve by division into small steps. This error term keeps on increasing with every step, and does not ensure high accuracy. The Runge-Kutta method however, has a very ingenious modification to this method, which makes it much more powerful by reducing error through RK4 by magnitudes of the order of 105. The modification that is made is to cancel out the error in every last step of the process.

This is done by using the trial step just as in the Euler method: The last term is the error term associated with the second step, and it is much lower than the one in Euler Method. This form of Runge-Kutta is known as RK2. To reduce error further, further step error reduction formulae are used, which involve different coefficients of the higher order error terms. These are formulated in RK4 or 4th order RK method as: The table clearly shows how low the error percentage in the RK4 method is. This shows the power of the method, though it is to be made known that this is not the most powerful of all methods.

But still, its ease of usage makes it the most common technique and the best choice when very high accuracy is not