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annotate +time/+rkparameters/rk6.m @ 1333:0aefcb30cab4 feature/D2_boundary_opt

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Add support for RK6
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Sat, 07 May 2022 10:30:59 +0200
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0aefcb30cab4 Add support for RK6
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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1 function [a,b,c,s] = rk6()
0aefcb30cab4 Add support for RK6
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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2 % Runge-Kutta 6 from Alshina07
0aefcb30cab4 Add support for RK6
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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3 s = 7;
0aefcb30cab4 Add support for RK6
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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4 a = sparse(s,s-1);
0aefcb30cab4 Add support for RK6
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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5 a(2,1) = 4/7;
0aefcb30cab4 Add support for RK6
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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6 a(3,1) = 115/112; a(3,2) = -5/16;
0aefcb30cab4 Add support for RK6
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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7 a(4,1) = 589/630; a(4,2) = 5/18; a(4,3) = -16/45;
0aefcb30cab4 Add support for RK6
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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8 a(5,1) = 229/1200 - 29/6000*sqrt(5); a(5,2) = 119/240 - 187/1200*sqrt(5); a(5,3) = -14/75 + 34/375*sqrt(5); a(5,4) = -3/100*sqrt(5);
0aefcb30cab4 Add support for RK6
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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9 a(6,1) = 71/2400 - 587/12000*sqrt(5); a(6,2) = 187/480 - 391/2400*sqrt(5); a(6,3) = -38/75 + 26/375*sqrt(5); a(6,4) = 27/80 - 3/400*sqrt(5); a(6,5) = (1+sqrt(5))/4;
0aefcb30cab4 Add support for RK6
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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10 a(7,1) = -49/480 + 43/160*sqrt(5); a(7,2) = -425/96 + 51/32*sqrt(5); a(7,3) = 52/15 - 4/5*sqrt(5); a(7,4) = -27/16 + 3/16*sqrt(5); a(7,5) = 5/4 - 3/4*sqrt(5); a(7,6) = 5/2 - 1/2*sqrt(5);
0aefcb30cab4 Add support for RK6
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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11 b = [1/12; 0; 0; 0; 5/12; 5/12; 1/12];
0aefcb30cab4 Add support for RK6
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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12 c = [0; 4/7; 5/7; 6/7; (5-sqrt(5))/10; (5+sqrt(5))/10; 1];
0aefcb30cab4 Add support for RK6
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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