chapter5.page13

# chapter5.page13 - ﬁrst transform an higher order...

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4. NUMERICAL METHOD FOR SYSTEM OF EQUATIONS 13 Similarly, we can use the same Mathcad code of Runge-Kutta method to find approximate solution as shown in the following screen shot for the above system of equations, Figure 8. Runge-Kutta’s method for system of equations 4.1. Numerical Method for Higher Order Equations. To find numerical approximate for solutions of higher order differential equations using either Euler’s method or Runge-Kutta method, we
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Unformatted text preview: ﬁrst transform an higher order diﬀerential equations into a system of ﬁrst order diﬀerential equations and then apply the methods. Example 4.2 . Rayleigh Equation In modeling the oscillations of a clarinet reed. Lord Rayleigh introduced an equation of the form mx 00 + kx = ax-b ( x ) 3 Find approximate solution for m = 1 ,k = 1 ,a = 2 ,b = 3 . and initial conditions x (0) = 1 ,x (0) =-2...
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