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annotate +rv/+time/BdfDerivative.m @ 1195:a4c00628a39d feature/rv

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Add higher order approximations to BDFDerivative
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 07 Aug 2019 13:27:36 +0200
parents 010bb2677230
children
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1016
4b42999874c0 Add lower level for boot-strapping to RungeKuttaExteriorRV
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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1 classdef BdfDerivative < handle
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eb441fbdf379 Draft implementation of RungeKutta with exterior RV updates
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2 properties
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e547794a9407 Add boot-strapping to RungeKuttaExteriorRV
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3 coefficients
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eb441fbdf379 Draft implementation of RungeKutta with exterior RV updates
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4 end
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010bb2677230 Clean up in +rv/+time. Make the time stepping more efficient by not storing unnessecary properties in the RK-RV time steppers
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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5 methods
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4b42999874c0 Add lower level for boot-strapping to RungeKuttaExteriorRV
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6 function obj = BdfDerivative()
4b42999874c0 Add lower level for boot-strapping to RungeKuttaExteriorRV
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7 obj.coefficients = obj.getBdfCoefficients();
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8 end
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e547794a9407 Add boot-strapping to RungeKuttaExteriorRV
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9 function DvDt = evaluate(obj, v, v_prev, dt)
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10 order = size(v_prev,2);
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11 DvDt = (obj.coefficients(order,1)*v - sum(obj.coefficients(order,2:order+1).*v_prev,2))/dt;
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12 end
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13 end
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14 methods(Static)
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4b42999874c0 Add lower level for boot-strapping to RungeKuttaExteriorRV
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15 function c = getBdfCoefficients()
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a4c00628a39d Add higher order approximations to BDFDerivative
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16 c = zeros(9,10);
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17 c(1,1) = 1; c(1,2) = 1;
a4c00628a39d Add higher order approximations to BDFDerivative
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18 c(2,1) = 3; c(2,2) = 4; c(2,3) = -1;
a4c00628a39d Add higher order approximations to BDFDerivative
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19 c(3,1) = 11; c(3,2) = 18; c(3,3) = -9; c(3,4) = 2;
a4c00628a39d Add higher order approximations to BDFDerivative
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20 c(4,1) = 25; c(4,2) = 48; c(4,3) = -36; c(4,4) = 16; c(4,5) = -3;
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21 c(5,1) = 137; c(5,2) = 300; c(5,3) = -300; c(5,4) = 200; c(5,5) = -75; c(5,6) = 12;
a4c00628a39d Add higher order approximations to BDFDerivative
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22 c(6,1) = 147; c(6,2) = 360; c(6,3) = -450; c(6,4) = 400; c(6,5) = -225; c(6,6) = 72; c(6,7) = -10;
a4c00628a39d Add higher order approximations to BDFDerivative
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1152
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23 % Note: Higher orders than 6 are not stable, but can still be used as one-sided approximations of a derivatve
a4c00628a39d Add higher order approximations to BDFDerivative
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1152
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24 c(7,1) = 1089; c(7,2) = 2940; c(7,3) = -4410; c(7,4) = 4900; c(7,5) = -3675; c(7,6) = 1764; c(7,7) = -490; c(7,8) = 60;
a4c00628a39d Add higher order approximations to BDFDerivative
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1152
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25 c(8,1) = 2283; c(8,2) = 6720; c(8,3) = -11760; c(8,4) = 15680; c(8,5) = -14700; c(8,6) = 9408; c(8,7) = -3920; c(8,8) = 960; c(8,9) = -105;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1152
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26 c(9,1) = 7129; c(9,2) = 22680; c(9,3) = -45360; c(9,4) = 70560; c(9,5) = -79380; c(9,6) = 63504; c(9,7) = -35280; c(9,8) = 12960; c(9,9) = -2835; c(9,10) = 280;
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parents: 1152
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27
a4c00628a39d Add higher order approximations to BDFDerivative
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1152
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28 % Scale coefficients
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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29 c(2,:) = c(2,:)/2;
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30 c(3,:) = c(3,:)/6;
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31 c(4,:) = c(4,:)/12;
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32 c(5,:) = c(5,:)/60;
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33 c(6,:) = c(6,:)/60;
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parents: 1152
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34 c(7,:) = c(7,:)/420;
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1152
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35 c(8,:) = c(8,:)/840;
a4c00628a39d Add higher order approximations to BDFDerivative
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1152
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36 c(9,:) = c(9,:)/2520;
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eb441fbdf379 Draft implementation of RungeKutta with exterior RV updates
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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37 end
eb441fbdf379 Draft implementation of RungeKutta with exterior RV updates
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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38 end
eb441fbdf379 Draft implementation of RungeKutta with exterior RV updates
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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39 end