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annotate +time/+rk/rungekutta_4.m @ 887:50d5a3843099 feature/timesteppers

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Rename package rk4 to rk
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 15 Nov 2018 16:42:58 -0800
parents +time/+rk4/rungekutta_4.m@48b6fb693025
children
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48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
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1 % Takes one time step of size k using the rungekutta method
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
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2 % starting from v_0 and where the function F(v,t) gives the
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
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3 % time derivatives.
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
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4 function v = rungekutta_4(v, t , k, F)
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
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5 k1 = F(v ,t );
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
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6 k2 = F(v+0.5*k*k1,t+0.5*k);
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
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7 k3 = F(v+0.5*k*k2,t+0.5*k);
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
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8 k4 = F(v+ k*k3,t+ k);
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
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9 v = v + (1/6)*(k1+2*(k2+k3)+k4)*k;
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
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10 end