Runge-Kutta 4th Order

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peny lin
peny lin on 31 May 2018
I have to solve mx"+cx'+kx=kc*[x(t-T)-x(t)] for milling problem, how can I apply Runge-Kutta method. Now the method I use us to calculate the force for each time steps, and x" can be written in x"=(f(t)-kx-cx')/m, and x'(i+1)=x'(i)+x"*dt, where dt is the time step. Then x(i+1)=x(i)+x'*dt. How can I reply Runge-Kutta for this problem. I can get the force at different time step to get k1 k2 k3 k4 for Runge-kutta, then get the x'(i+1)=x(i)+1/6(k1+2*k2+2*k3+k4)? and calculate the x' at different time step for k1 k2 k3 k4 to get x(i)=x(i+1)+1/6(k1+2*k2+2*k3+k4)? Is my idea wrong? Or matlab provide any other better ways to sole the time delay differentiation equation? Thank you very much.

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