Solving First order ODEs simultaneously

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Valerie 2023-9-28

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2027009-solving-first-order-odes-simultaneously

评论： Valerie 2023-9-29

Hello, needed help figuring out why I cannot obtain a solution. I'm sure this is a solvable solution however I keep getting a warning saying no solution is found. Is there any mistake I'm making in the code?

Everything is a constant except E, Sr(t) & Er(t).

% Rigorous Solution Case #1
syms Sr(t) Er(t) E;
E = Ea - Er(t);
Unrecognized function or variable 'Ea'.
ode2a = diff(Sr(t),t) == -(k1*(Ea - Er(t))*Sr(t)) + krev1*Er(t);
ode3a = diff(Er,t) == (k1*(Ea - Er(t))*Sr(t)) - (krev1+k2)*Er(t);
odes = [ode2a; ode3a];
cond1 = Sr(0) == Sa;
cond2 = Er(0) == 0;
conds = [cond1; cond2];
[SrSol(t),ErSol(t)] = dsolve(odes,conds)

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Walter Roberson 2023-9-28

在 MATLAB Online 中打开

Ea = 123; %just to have SOME value

k1 = 42; %just to have SOME value

k2 = 13; %just to have SOME value

krev1 = 48; %just to have SOME value

Sa = 5; %just to have SOME value

% Rigorous Solution Case #1

syms Sr(t) Er(t) E;

E = Ea - Er(t);

ode2a = diff(Sr(t),t) == -(k1*(Ea - Er(t))*Sr(t)) + krev1*Er(t);

ode3a = diff(Er,t) == (k1*(Ea - Er(t))*Sr(t)) - (krev1+k2)*Er(t);

eqns = [ode2a; ode3a];

cond1 = Sr(0) == Sa;

cond2 = Er(0) == 0;

conds = [cond1; cond2];

[eqs,vars] = reduceDifferentialOrder(eqns, [Sr(t), Er(t)])

eqs =

vars =

[M,F] = massMatrixForm(eqs,vars)

M =

F =

f = M\F

f =

odefun = odeFunction(f,vars)

odefun = function_handle with value:

@(t,in2)[in2(2,:).*4.8e+1-in2(1,:).*5.166e+3+in2(2,:).*in2(1,:).*4.2e+1;in2(2,:).*-6.1e+1+in2(1,:).*5.166e+3-in2(2,:).*in2(1,:).*4.2e+1]

InitConditions = double(rhs(conds)) %watch out for order though!

InitConditions = 2×1

5 0

[T, Y] = ode45(odefun, [0 0.01], InitConditions);

subplot(2,1,1); plot(T, Y(:,1)); title(string(vars(1)))

subplot(2,1,2); plot(T, Y(:,2)); title(string(vars(2)))

%that almost looks like the initial conditions are reversed.

%what happens if we try reversing the conditions?

[Tr, Yr] = ode45(odefun, [0 0.01], flipud(InitConditions));

figure

subplot(2,1,1); plot(Tr, Yr(:,1)); title(string(vars(1)))

subplot(2,1,2); plot(Tr, Yr(:,2)); title(string(vars(2)))

Valerie 2023-9-28

Thank you so much!

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采纳的回答

Torsten 2023-9-28

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2027009-solving-first-order-odes-simultaneously#answer_1321289

移动：Torsten 2023-9-28

I'm quite sure there is no analytical solution for your system of ODEs since the right-hand sides are nonlinear in the unknown functions (term Er(t)*Sr(t)).