Find Coefficients of a 5th order ODE without ode45
3 vues (au cours des 30 derniers jours)
Afficher commentaires plus anciens
The code below I came up with, I am getting the correct roots but the constants are wrong and the graph is not correct either. Can you please help me figure out why it's coming out incorrect.
%Eqn: y'''''-5y'''+4y' = 0
format long
Coefa = 1;
Coefb = 0;
Coefc = -5;
Coefd = 0;
Coefe = 4;
Coeff = 0;
x0 = 0; Yin = 3, Yder1 = -5, Yder2 = 11 , Yder3 = -23, Yder4 = 47,
B = [Yin Yder1 Yder2 , Yder3 Yder4]; N = 1000;
x = linspace(0,25,N);
y = zeros(1,N);
R = zeros(1,4);
R = SecondOderODE1(Coefa,Coefb, Coefc,Coefd, Coefe,Coeff);
if abs(R(1)-R(4))>=1/10^6
A = [exp(R(1).*x0), exp(R(2).*x0), exp(R(3).*x0), exp(R(4).*x0), exp(R(5).*x0); exp(x0.*R(1)).*R(1), R(2).*exp(x0.*R(2)), exp(x0.*R(3)).*R(3), exp(x0.*R(4)).*R(4), exp(x0.*R(5)).*R(5)];
C = B./A
for i = 1:1:N
y(i) = real(C(1)*exp(R(1)*x(i)) + C(2)*exp(R(2)*x(i)))+ C(3)*exp(R(3)*x(i))+ C(4)*exp(R(4)*x(i))+ C(5)*exp(R(5)*x(i));
figure(1)
plot (x,y)
xlabel ('x')
ylabel('y')
grid on
end
end
figure(1)
plot(x,y)
xlabel ('x')
ylabel('y')
grid on
0 commentaires
Réponse acceptée
Torsten
le 22 Oct 2023
syms t x(t)
Dx = diff(x,t);
D2x = diff(x,t,2);
D3x = diff(x,t,3);
D4x = diff(x,t,4);
D5x = diff(x,t,5);
eqn = D5x-5*D3x+4*Dx == 0;
conds = [x(0) == 3,Dx(0) == -5,D2x(0) ==11, D3x(0) == -23, D4x(0)==47];
sol = dsolve(eqn,conds)
fplot(sol,[0 1])
4 commentaires
Torsten
le 22 Oct 2023
Modifié(e) : Torsten
le 22 Oct 2023
The roots could be complex-valued or a root could be of higher order than 1. How do you handle this with your code ?
In short: a solution without dsolve or ODE45 will get much more complex than the code you posted.
For the equation posted, a paper-and-pencil solution will be easiest - and it doesn't use ODE45 or dsolve :-)
Plus de réponses (0)
Voir également
Catégories
En savoir plus sur Ordinary Differential Equations dans Help Center et File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!