Why Matlab could not solve a set of linear differential equations with initial conditions through dsolve?
2 Ansichten (letzte 30 Tage)
Ältere Kommentare anzeigen
Hi,
Where is the problem in my codes to solve a set of linear differential equations with initial conditions?
Any suggest?
clc
clear
ML = [2.53735261480440e-10 -1.35406667270221e-16 1.30871725825994e-18 -2.13374675288863e-15 2.03261768716403e-17 -1.61477754970584e-16 -1.62541250675724e-16;
-1.35406667270221e-16 2.53734628229043e-10 -2.73582082145325e-17 4.72489571641653e-16 1.92706132643316e-16 8.27766626176449e-16 -4.33522241607763e-16;
1.30871725825994e-18 -2.73582082145325e-17 2.53811694377620e-10 -1.38664722187494e-14 1.89471206077083e-13 -5.47669811839268e-14 2.67184290813528e-14;
-2.13374675288863e-15 4.72489571641653e-16 -1.38664722187494e-14 2.53715763347126e-10 -6.05035598297774e-15 -2.32344311157266e-14 2.96103830935012e-14;
2.03261768716403e-17 1.92706132643316e-16 1.89471206077083e-13 -6.05035598297774e-15 2.53850804700165e-10 -6.82222668978547e-14 4.82767908961758e-14;
-1.61477754970584e-16 8.27766626176449e-16 -5.47669811839268e-14 -2.32344311157266e-14 -6.82222668978547e-14 2.53705685445938e-10 3.43519159646703e-14;
-1.62541250675724e-16 -4.33522241607763e-16 2.67184290813528e-14 2.96103830935012e-14 4.82767908961758e-14 3.43519159646703e-14 2.53690028388901e-10];
KL = [6.34368385323866e-05 -5.80205835437760e-08 -1.23764005930491e-10 -1.48354797737571e-07 -3.76339592244736e-08 -1.55516201961077e-07 -2.99714848304693e-07;
-5.80205835437760e-08 0.00277423390772568 -3.64032926965371e-10 -1.15677999366471e-06 -5.05159524190059e-07 -1.14803879509422e-06 -2.36449328010142e-06;
-1.23764005930491e-10 -3.64032926965371e-10 0.00351253253565176 2.60553493225360e-07 -2.50880577858935e-05 8.96289108975872e-06 2.53253964466067e-07;
-1.48354797737571e-07 -1.15677999366471e-06 2.60553493225360e-07 0.0201021660593748 -0.000292315163965329 0.000101788069022335 -6.31134009698694e-06;
-3.76339592244736e-08 -5.05159524190059e-07 -2.50880577858935e-05 -0.000292315163965329 0.0414826409114255 0.00570625287068793 0.00236501515779697;
-1.55516201961077e-07 -1.14803879509422e-06 8.96289108975872e-06 0.000101788069022335 0.00570625287068793 0.0634851951853710 -0.000910774592712826;
-2.99714848304693e-07 -2.36449328010142e-06 2.53253964466067e-07 -6.31134009698694e-06 0.00236501515779697 -0.000910774592712826 0.121679411312940];
F=[0.000289760052925726;
0.000537710491736623;
1.24507643858810e-08;
-0.000328931258625777;
-4.51634984307082e-05;
-0.000110003762488177;
-0.000505551160254736];
syms tau_1(t) tau_2(t) tau_3(t) tau_4(t) tau_5(t) tau_6(t) tau_7(t)
v = transpose([tau_1 tau_2 tau_3 tau_4 tau_5 tau_6 tau_7]);
odes = diff(diff(v)) == -inv(ML) * KL * v;
C = [v(0) == double(0*inv(ML) * [F]) , diff(v(0)) == double(01*inv(ML) * [F])];
dsolve(odes,C)
0 Kommentare
Akzeptierte Antwort
Torsten
am 12 Nov. 2022
Bearbeitet: Torsten
am 12 Nov. 2022
The eigenvalues of a polynomial of degree 14 (=degree of ODEs * number of ODEs) are required to get an analytical solution for your problem. But analytical formulae for roots of polynomials only exist up to degree 4.
4 Kommentare
Torsten
am 12 Nov. 2022
Bearbeitet: Torsten
am 12 Nov. 2022
ML = [2.53735261480440e-10 -1.35406667270221e-16 1.30871725825994e-18 -2.13374675288863e-15 2.03261768716403e-17 -1.61477754970584e-16 -1.62541250675724e-16;
-1.35406667270221e-16 2.53734628229043e-10 -2.73582082145325e-17 4.72489571641653e-16 1.92706132643316e-16 8.27766626176449e-16 -4.33522241607763e-16;
1.30871725825994e-18 -2.73582082145325e-17 2.53811694377620e-10 -1.38664722187494e-14 1.89471206077083e-13 -5.47669811839268e-14 2.67184290813528e-14;
-2.13374675288863e-15 4.72489571641653e-16 -1.38664722187494e-14 2.53715763347126e-10 -6.05035598297774e-15 -2.32344311157266e-14 2.96103830935012e-14;
2.03261768716403e-17 1.92706132643316e-16 1.89471206077083e-13 -6.05035598297774e-15 2.53850804700165e-10 -6.82222668978547e-14 4.82767908961758e-14;
-1.61477754970584e-16 8.27766626176449e-16 -5.47669811839268e-14 -2.32344311157266e-14 -6.82222668978547e-14 2.53705685445938e-10 3.43519159646703e-14;
-1.62541250675724e-16 -4.33522241607763e-16 2.67184290813528e-14 2.96103830935012e-14 4.82767908961758e-14 3.43519159646703e-14 2.53690028388901e-10];
KL = [6.34368385323866e-05 -5.80205835437760e-08 -1.23764005930491e-10 -1.48354797737571e-07 -3.76339592244736e-08 -1.55516201961077e-07 -2.99714848304693e-07;
-5.80205835437760e-08 0.00277423390772568 -3.64032926965371e-10 -1.15677999366471e-06 -5.05159524190059e-07 -1.14803879509422e-06 -2.36449328010142e-06;
-1.23764005930491e-10 -3.64032926965371e-10 0.00351253253565176 2.60553493225360e-07 -2.50880577858935e-05 8.96289108975872e-06 2.53253964466067e-07;
-1.48354797737571e-07 -1.15677999366471e-06 2.60553493225360e-07 0.0201021660593748 -0.000292315163965329 0.000101788069022335 -6.31134009698694e-06;
-3.76339592244736e-08 -5.05159524190059e-07 -2.50880577858935e-05 -0.000292315163965329 0.0414826409114255 0.00570625287068793 0.00236501515779697;
-1.55516201961077e-07 -1.14803879509422e-06 8.96289108975872e-06 0.000101788069022335 0.00570625287068793 0.0634851951853710 -0.000910774592712826;
-2.99714848304693e-07 -2.36449328010142e-06 2.53253964466067e-07 -6.31134009698694e-06 0.00236501515779697 -0.000910774592712826 0.121679411312940];
F=[0.000289760052925726;
0.000537710491736623;
1.24507643858810e-08;
-0.000328931258625777;
-4.51634984307082e-05;
-0.000110003762488177;
-0.000505551160254736];
ML_invers = inv(ML);
fun = @(t,v)[v(8:14);-ML_invers * KL * v(1:7)];
v0 = [0*ML_invers * F;1*ML_invers * F];
[T,V] = ode15s(fun,[0 0.015],v0);
plot(T,V(:,1))
Weitere Antworten (0)
Siehe auch
Kategorien
Mehr zu Symbolic Math Toolbox finden Sie in Help Center und File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!