Question #108302
Using the classical fourth order Runge-Kutta method, find the approximate value of y(0.6) for the initial value problem dy/dx = sin xy ; y(0) =1 with the step size h =0.2
1
Expert's answer
2020-04-13T12:50:59-0400
yn+1=yn+h(k16+k23+k33+k46)y_{n+1}=y_n+h(\frac {k_1}{6}+\frac{k_2}{3}+\frac{k_3}{3}+\frac {k_4}{6})


xn+1=xn+hx_{n+1}=x_n+h


k1=f(xn;yn)k_1=f(x_n;y_n)


k2=f(xn+h2;yn+hk12)k_2=f(x_n+\frac{h}{2}; y_n+\frac {hk_1}{2})


k3=f(xn+h3;yn+hk22)k_3=f(x_n+\frac{h}{3}; y_n+\frac {hk_2}{2})


k4=f(xn+h;yn+hk3)k_4=f(x_n+h; y_n+hk_3)






Stability function:

z424+z36+z22+z+1\frac{z^4}{24}+\frac{z^3}{6}+\frac{z^2}{2}+z+1


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