try to obtain estimates of the value of y when x = 1.6 by using each of :
(i)Euler’s method,
(ii)The fourth-order Runge-Kutta method :
Yn+1 = Yn + 1/6(k1+ 2K2+2k3=k4)
Where
k1= hf(Xn,Yn)
k2= hf(Xn+1/2h ,Yn+ 1/2K1)
k3= hf(Xn+1/2h ,Yn+ 1/2K2)
k4= hf(Xn+h ,Yn+K3)
Find the exact solution of the above O.D.E.. How does the exact value of y when x = 1.6 compare with your estimates obtained in (a) ? Would you expect the results you would have obtained if you had used a smaller step size (e.g. h = 0.1 or h = 0.05) to have been much better ? Explain your answer.
how do you do this
2006-11-29
08:14:50
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4 answers
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asked by
Glendon
1
in
Mathematics