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annotate +time/+rk/rungekutta.m @ 888:8732d6bd9890 feature/timesteppers

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Add general Runge-Kutta class - Add a general Runge-Kutta class which time integrates the solution based on coefficients obtained from a Butcher tableau - Add butcher tableau which returns coefficents for the specified Runge-Kutta method - Remove RungKutta4proper, since obsolete
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 15 Nov 2018 17:10:01 -0800
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children 878652b22157
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8732d6bd9890 Add general Runge-Kutta class
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 function v = rungekutta(v, t , dt, F, coeffs)
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6 % Compute the intermediate stages k
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7 k = zeros(length(v), coeffs.s);
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8 for i = 1:coeffs.s
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9 u = v;
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10 for j = 1:i-1
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11 u = u + dt*coeffs.a(i,j)*k(:,j);
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12 end
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13 k(:,i) = F(u,t+coeffs.c(i)*dt);
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14 end
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15 % Compute the updated solution as a linear combination
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16 % of the intermediate stages.
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17 for i = 1:coeffs.s
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18 v = v + dt*coeffs.b(i)*k(:,i);
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19 end
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20 end