annotate +time/+rk4/rungekutta_4.m @ 1198:2924b3a9b921
feature/d2_compatible
Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
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Martin Almquist <malmquist@stanford.edu> |
| date |
Fri, 16 Aug 2019 14:30:28 -0700 |
| parents |
48b6fb693025 |
| children |
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| rev |
line source |
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1 % Takes one time step of size k using the rungekutta method
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2 % starting from v_0 and where the function F(v,t) gives the
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3 % time derivatives.
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4 function v = rungekutta_4(v, t , k, F)
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5 k1 = F(v ,t );
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6 k2 = F(v+0.5*k*k1,t+0.5*k);
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7 k3 = F(v+0.5*k*k2,t+0.5*k);
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8 k4 = F(v+ k*k3,t+ k);
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9 v = v + (1/6)*(k1+2*(k2+k3)+k4)*k;
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10 end |
