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Simple_runge_kutta_example

Simple_runge_kutta_example - Simple Runge-Kutta solution of...

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Simple Runge-Kutta solution of an ODE J. M. Cimbala, September 2001 The equation to be solved is dy/dt = B - Ay, where in general A and B can be functions of time. The data are plotted on a separate sheet called "plot of y vs t". tstart = 0 deltat = 0.01 y(tstart) = 7.6 ti yi A(t) B(t) Di ta ya Da tb yb Db yc Dc yi+1 0 7.6 3.82 10 -19.03 0.01 7.5 -18.67 0.01 7.51 -18.68 7.41 -18.32 7.41 0.01 7.41 3.82 10 -18.32 0.02 7.32 -17.97 0.02 7.32 -17.98 7.23 -17.63 7.23 0.02 7.23 3.82 10 -17.63 0.03 7.15 -17.3 0.03 7.15 -17.3 7.06 -16.97 7.06 0.03 7.06 3.82 10 -16.97 0.04 6.98 -16.65 0.04 6.98 -16.65 6.89 -16.34 6.89 0.04 6.89 3.82 10 -16.34 0.05 6.81 -16.02 0.05 6.81 -16.03 6.73 -15.72 6.73 0.05 6.73 3.82 10 -15.72 0.06 6.66 -15.42 0.06 6.66 -15.43 6.58 -15.13 6.58 0.06 6.58 3.82 10 -15.13 0.07 6.5 -14.84 0.07 6.51 -14.85 6.43 -14.57 6.43 0.07 6.43 3.82 10 -14.57 0.08 6.36 -14.29 0.08 6.36 -14.29 6.29 -14.02 6.29 0.08 6.29 3.82 10 -14.02 0.09 6.22 -13.75 0.09 6.22 -13.76 6.15 -13.49 6.15 0.09 6.15 3.82 10 -13.5 0.1 6.08 -13.24 0.1 6.08 -13.24 6.02 -12.99 6.02 0.1 6.02 3.82 10 -12.99 0.11 5.95 -12.74 0.11 5.95 -12.75 5.89 -12.5 5.89 0.11 5.89 3.82 10 -12.5 0.12 5.83 -12.26 0.12 5.83 -12.27 5.77 -12.03 5.77 0.12 5.77 3.82 10 -12.03 0.13 5.71 -11.8 0.13 5.71 -11.81 5.65 -11.58 5.65 0.13 5.65 3.82 10 -11.58 0.14 5.59 -11.36 0.14 5.59 -11.37 5.54 -11.15 5.54 0.14 5.54 3.82 10 -11.15 0.15 5.48 -10.94 0.15 5.48 -10.94 5.43 -10.73 5.43 0.15 5.43 3.82 10 -10.73 0.16 5.37 -10.53 0.16 5.37 -10.53 5.32 -10.33 5.32 0.16 5.32 3.82 10 -10.33 0.17 5.27 -10.13 0.17 5.27 -10.14 5.22 -9.94 5.22 0.17 5.22 3.82 10 -9.94 0.18 5.17 -9.75 0.18 5.17 -9.76 5.12 -9.57 5.12 0.18 5.12 3.82 10 -9.57 0.19 5.07 -9.39 0.19 5.08 -9.39 5.03 -9.21 5.03 0.19 5.03 3.82 10 -9.21 0.2 4.98 -9.03 0.2 4.98 -9.04 4.94 -8.87 4.94 0.2 4.94 3.82 10 -8.87 0.21 4.89 -8.7 0.21 4.9 -8.7 4.85 -8.53 4.85 0.21 4.85 3.82 10 -8.53 0.22 4.81 -8.37 0.22 4.81 -8.37 4.77 -8.21 4.77 0.22 4.77 3.82 10 -8.21 0.23 4.73 -8.06 0.23 4.73 -8.06 4.69 -7.91 4.69 0.23 4.69 3.82 10 -7.91 0.24 4.65 -7.75 0.24 4.65 -7.76 4.61 -7.61 4.61 0.24 4.61 3.82 10 -7.61 0.25 4.57 -7.46 0.25 4.57 -7.47 4.54 -7.32 4.54 0.25 4.54 3.82 10 -7.32 0.26 4.5 -7.18 0.26 4.5 -7.19 4.46 -7.05 4.46 0.26 4.46 3.82 10 -7.05 0.27 4.43 -6.91 0.27 4.43 -6.92 4.39 -6.79 4.39 0.27 4.39 3.82 10 -6.79 0.28 4.36 -6.66 0.28 4.36 -6.66 4.33 -6.53 4.33 0.28 4.33 3.82 10 -6.53 0.29 4.29 -6.41 0.29 4.3 -6.41 4.26 -6.29 4.26 0.29 4.26 3.82 10 -6.29 0.3 4.23 -6.17
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