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annotate +time/+rk/rungekutta.m @ 985:ad6de007e7f6 feature/timesteppers

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Convert Rungekutta4SecondOrder to take F(t,v,v_t) instead of matrices
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 08 Jan 2019 12:34:29 +0100
parents 878652b22157
children
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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1 % Takes one time step of size dt using the rungekutta method
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2 % starting from @arg v and where the function F(v,t) gives the
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3 % time derivatives. coeffs is a struct holding the RK coefficients
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4 % for the specific method.
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5 % Also returns the stage approximations (V) and stage rates (K).
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6 function [v, V, K] = rungekutta(v, t , dt, F, coeffs)
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7 % Compute the intermediate stages k
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8 K = zeros(length(v), coeffs.s);
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9 V = zeros(length(v), coeffs.s);
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10 for i = 1:coeffs.s
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11 u = v;
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12 for j = 1:i-1
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13 u = u + dt*coeffs.a(i,j)*K(:,j);
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14 end
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15 V(:,i) = u;
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16 K(:,i) = F(u,t+coeffs.c(i)*dt);
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17 end
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18 % Compute the updated solution as a linear combination
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19 % of the intermediate stages.
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20 for i = 1:coeffs.s
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21 v = v + dt*coeffs.b(i)*k(:,i);
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22 end
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23 end