Setting assumptions for a function when solving system of ODEs
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I have a following code below that is supposed to solve a dynamic system. I am trying to restrict X3(t) to be less than or equal to 0.1 (a saturation point). So I added a line about assumption for X3(t). However, it seems like assume command is not possible for symbolic functions. How should I get this done?
syms t A B kEuT kTEu X1(t) X2(t) X3(t) X4(t) X5(t) X6(t)
eqn1 = diff(X1) == -B*X1 + A*X2 eqn2 = diff(X2) == -(A+kEuT)*X2 + B*X1 + kTEu*X3 eqn3 = diff(X3) == kEuT*X2 - kTEu*X3 C1 = X1(-20) == 1 C2 = X2(-20) == 0 C3 = X3(-20) == 0 assume(X3 <= 0.1) [X1S(t) X2S(t) X3S(t)] = dsolve(eqn1, eqn2, eqn3, C1, C2, C3) X1Sc = simplify(combine(X1S(t)),'IgnoreAnalyticConstraints',true) X2Sc = simplify(combine(X2S(t)),'IgnoreAnalyticConstraints',true) X3Sc = simplify(combine(X3S(t)),'IgnoreAnalyticConstraints',true)
eqn4 = diff(X4) == A*X5 eqn5 = diff(X5) == -(A+kEuT)*X5 + kTEu*X6 eqn6 = diff(X6) == kEuT*X5 - kTEu*X6 C4 = X4(0) == X1S(0) C5 = X5(0) == X2S(0) C6 = X6(0) == X3S(0) [X4S(t) X5S(t) X6S(t)] = dsolve(eqn4, eqn5, eqn6, C4, C5, C6) X4Sc = simplify(combine(X4S(t)),'IgnoreAnalyticConstraints',true) X5Sc = simplify(combine(X5S(t)),'IgnoreAnalyticConstraints',true) X6Sc = simplify(combine(X6S(t)),'IgnoreAnalyticConstraints',true)
X1Sc = vpa(subs(X1Sc, [A, B, kEuT, kTEu], [2000000, 1000000, 20000, 100])) X2Sc = vpa(subs(X2Sc, [A, B, kEuT, kTEu], [2000000, 1000000, 20000, 100])) X3Sc = vpa(subs(X3Sc, [A, B, kEuT, kTEu], [2000000, 1000000, 20000, 100])) X4Sc = vpa(subs(X4Sc, [A, B, kEuT, kTEu], [2000000, 1000000, 20000, 100])) X5Sc = vpa(subs(X5Sc, [A, B, kEuT, kTEu], [2000000, 1000000, 20000, 100])) X6Sc = vpa(subs(X6Sc, [A, B, kEuT, kTEu], [2000000, 1000000, 20000, 100]))
x1 = linspace(-20,0,200) X1Scp = subs(X1Sc, t, x1) X2Scp = subs(X2Sc, t, x1) X3Scp = subs(X3Sc, t, x1) x2 = linspace(0,20,200) X4Scp = subs(X4Sc, t, x2) X5Scp = subs(X5Sc, t, x2) X6Scp = subs(X6Sc, t, x2)
plot(x1,X1Scp,'b',x1,X2Scp,'k',x1,X3Scp','r',x2,X4Scp,'b',x2,X5Scp,'k',x2,X6Scp,'r'), xlabel('time/s'),ylabel('population density'),axis([-20 20 0 0.01])
Thank you
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Nicolas Mira Gebauer
le 10 Août 2020
Hi, how did you solve this problem?
I am currently stuck at something similar..
Thank you in advance
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