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Rohit K

Guest

Need solutions using Runge Kutta fourth order method

Q) Given that dy/dx=y-x with y(0) = 2, find y(0.1) and y(0.2) correct upto four decimal, using Runge Kutta fourth order method.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,837

Re: Need solutions using Runge Kutta fourth order method

Hi Rohit K,

Welcome to the forum!

Introduction: : For the benefit of other members:

In numerical analysis, the Runge–Kutta methods are a family of implicit and explicit iterative methods, which include the well-known routine called the Euler Method, used in temporal discretization for the approximate solutions of ordinary differential equations. These methods were developed around 1900 by the German mathematicians Carl Runge and Wilhelm Kutta.

The most widely known member of the Runge–Kutta family is generally referred to as "RK4", the "classic Runge–Kutta method" or simply as "the Runge–Kutta method".

The RK4 method is a fourth-order method, meaning that the local truncation error is on the order of

, while the total accumulated error is on the order of

In many practical applications the function

is independent of

(so called autonomous system, or time-invariant system, especially in physics), and their increments are not computed at all and not passed to function

, with only the final formula for

used.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Need solutions using Runge Kutta fourth order method

hi Rohit K

Welcome to the forum.

It's always useful to know how much the student already knows before embarking on some help.  How much do you know about the second order method? Are you able to post an example of one you have successfully done?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob