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annotate +rv/+time/BDFDerivative.m @ 1013:eb441fbdf379 feature/advectionRV

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Draft implementation of RungeKutta with exterior RV updates - Draft class RungeKuttaExteriorRV which updates the residual using a BDF approximation of the derivtive outside of the RK stages. - Draft class for BDF derivative
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 05 Dec 2018 15:04:44 +0100
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children e547794a9407
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eb441fbdf379 Draft implementation of RungeKutta with exterior RV updates
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1 class BDFDerivative < handle
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2 properties
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3 dt
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4 coefficents
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5 end
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6 methods
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7 function obj = BDFDerivative(order, dt)
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8 obj.coefficents = obj.getBDFCoefficients(order);
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9 obj.dt = dt;
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10 end
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12 function DvDt = evaluate(v, v_prev)
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13 DvDt = (obj.coefficients(1)*v - sum(obj.coefficients(2:end).*v_prev),2)/obj.dt;
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14 end
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16 function c = getBDFCoefficients(obj, order)
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17 switch order
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18 case 1
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19 c(1,1) = 1; c(1,2) = 1;
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20 case 2
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21 c(1,1) = 3/2; c(1,2) = 4/2; c(1,3) = -1/2;
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22 case 3
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23 c(1,1) = 11/6; c(1,2) = 18/6; c(1,3) = -9/6; c(1,4) = 2/6;
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24 case 4
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25 c(1,1) = 25/12; c(1,2) = 48/12; c(1,3) = -36/12; c(1,4) = 16/12; c(1,5) = -3/12;
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26 case 5
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27 c(1,1) = 137/60; c(1,2) = 300/60; c(1,3) = -300/60; c(1,4) = 200/60; c(1,5) = -75/60; c(1,6) = 12/60;
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28 case 6
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29 c(1,1) = 147/60; c(1,2) = 360/60; c(1,3) = -450/60; c(1,4) = 400/60; c(1,5) = -225/60; c(1,6) = 72/60; c(1,7) = -10/60;
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30 assert(length(c) == (order+1));
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31 end
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32 end
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33 end