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changeset 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 bd5383809917
children f6c571d8f22f
files +rv/+time/BdfDerivative.m +rv/+time/RungekuttaRvBdf.m
diffstat 2 files changed, 22 insertions(+), 8 deletions(-) [+]
line wrap: on
line diff
diff -r bd5383809917 -r a4c00628a39d +rv/+time/BdfDerivative.m
--- a/+rv/+time/BdfDerivative.m	Mon Aug 05 10:45:08 2019 +0200
+++ b/+rv/+time/BdfDerivative.m	Wed Aug 07 13:27:36 2019 +0200
@@ -13,13 +13,27 @@
     end
     methods(Static)
         function c = getBdfCoefficients()
-            c = zeros(6,7);
-            c(1,1) = 1; c(1,2) = 1;
-            c(2,1) = 3/2; c(2,2) = 4/2; c(2,3) = -1/2;
-            c(3,1) = 11/6; c(3,2) = 18/6; c(3,3) = -9/6; c(3,4) = 2/6;
-            c(4,1) = 25/12; c(4,2) = 48/12; c(4,3) = -36/12; c(4,4) = 16/12; c(4,5) = -3/12;
-            c(5,1) = 137/60; c(5,2) = 300/60; c(5,3) = -300/60; c(5,4) = 200/60; c(5,5) = -75/60; c(5,6) = 12/60;
-            c(6,1) = 147/60; c(6,2) = 360/60; c(6,3) = -450/60; c(6,4) = 400/60; c(6,5) = -225/60; c(6,6) = 72/60; c(6,7) = -10/60;
+            c = zeros(9,10);
+            c(1,1) = 1;    c(1,2) = 1;
+            c(2,1) = 3;    c(2,2) = 4;     c(2,3) = -1;                     
+            c(3,1) = 11;   c(3,2) = 18;    c(3,3) = -9;     c(3,4) = 2;
+            c(4,1) = 25;   c(4,2) = 48;    c(4,3) = -36;    c(4,4) = 16;    c(4,5) = -3;
+            c(5,1) = 137;  c(5,2) = 300;   c(5,3) = -300;   c(5,4) = 200;   c(5,5) = -75;    c(5,6) = 12; 
+            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; 
+            % Note: Higher orders than 6 are not stable, but can still be used as one-sided approximations of a derivatve
+            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; 
+            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; 
+            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; 
+
+            % Scale coefficients
+            c(2,:) = c(2,:)/2;
+            c(3,:) = c(3,:)/6;
+            c(4,:) = c(4,:)/12;
+            c(5,:) = c(5,:)/60;
+            c(6,:) = c(6,:)/60;
+            c(7,:) = c(7,:)/420;
+            c(8,:) = c(8,:)/840;
+            c(9,:) = c(9,:)/2520;
         end
     end
 end
diff -r bd5383809917 -r a4c00628a39d +rv/+time/RungekuttaRvBdf.m
--- a/+rv/+time/RungekuttaRvBdf.m	Mon Aug 05 10:45:08 2019 +0200
+++ b/+rv/+time/RungekuttaRvBdf.m	Wed Aug 07 13:27:36 2019 +0200
@@ -29,7 +29,7 @@
             obj.RV = RV;
             obj.lowerBdfOrder = bdfOrders.lowerBdfOrder;
             obj.upperBdfOrder = bdfOrders.upperBdfOrder;
-            assert((obj.lowerBdfOrder >= 1) && (obj.upperBdfOrder <= 6));
+            assert((obj.lowerBdfOrder >= 1) && (obj.upperBdfOrder <= 9));
             obj.v_prev = [];
             obj.DvDt = rv.time.BdfDerivative();