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mws_gen_ode_txt_runge4th

# mws_gen_ode_txt_runge4th - Chapter 08.04 Runge-Kutta 4th...

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08.04.1 Chapter 08.04 Runge-Kutta 4th Order Method for Ordinary Differential Equations After reading this chapter, you should be able to 1. develop Runge-Kutta 4 th order method for solving ordinary differential equations, 2. find the effect size of step size has on the solution, 3. know the formulas for other versions of the Runge-Kutta 4 th order method What is the Runge-Kutta 4th order method? Runge-Kutta 4 th order method is a numerical technique used to solve ordinary differential equation of the form ( ) ( ) 0 0 , , y y y x f dx dy = = So only first order ordinary differential equations can be solved by using the Runge-Kutta 4 th order method. In other sections, we have discussed how Euler and Runge-Kutta methods are used to solve higher order ordinary differential equations or coupled (simultaneous) differential equations. How does one write a first order differential equation in the above form? Example 1 Rewrite ( ) 5 0 , 3 . 1 2 = = + y e y dx dy x in 0 ) 0 ( ), , ( y y y x f dx dy = = form.

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