6592cd058d
git-subtree-dir: octive-lean git-subtree-mainline:fd3d42ae33git-subtree-split:4b6fcec565
29 lines
734 B
Matlab
29 lines
734 B
Matlab
% Example 1: 1-D non-dim gravity
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% x' = v
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% v' = -1/x^2, x(0) = 1, v(0) = 0
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% RK4 fixed-step.
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n = 100;
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t0 = 0; tf = 1.0;
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h = (tf - t0) / n;
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t = zeros(1, n+1);
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xs = zeros(1, n+1);
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vs = zeros(1, n+1);
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xs(1) = 1.0;
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vs(1) = 0.0;
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for i = 1:n
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ti = t(i); xi = xs(i); vi = vs(i);
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k1x = vi; k1v = -1 / xi^2;
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k2x = vi + h/2*k1v; k2v = -1 / (xi + h/2*k1x)^2;
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k3x = vi + h/2*k2v; k3v = -1 / (xi + h/2*k2x)^2;
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k4x = vi + h*k3v; k4v = -1 / (xi + h*k3x)^2;
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t(i+1) = ti + h;
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xs(i+1) = xi + h/6 * (k1x + 2*k2x + 2*k3x + k4x);
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vs(i+1) = vi + h/6 * (k1v + 2*k2v + 2*k3v + k4v);
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endfor
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for i = 1:n+1
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printf("%f,%f,%f\n", t(i), xs(i), vs(i));
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endfor
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