Programming error with a model function

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Chatowa
Chatowa 2023-7-31
编辑： Torsten 2023-7-31
Ran in:
I don't understand why but I'm getting an error message regarding my Matlab script:
I'm trying to code for the example equation
y′1=y′2
y2=A/Bty1.
tspan = [0 5];
y0 = [0 0.1];
A = 1;
B = 2;
[t,yAB] = ode15s(@fun40,tspan,y0);
Unrecognized function or variable 'dyB'.

Error in solution>fun40 (line 11)
dyA(1) = dyB(2);

Error in odearguments (line 92)
f0 = ode(t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode15s (line 153)
odearguments(odeIsFuncHandle, odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);
figure
semilog(t,y)
grid
function dyAB = fun40(t,yAB)
dyAB = zeros(2,1);
dyA(1) = dyB(2);
dyB(2) = (A/B)*t.*dyA(1);
end

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采纳的回答

Torsten
Torsten 2023-7-31
编辑：Torsten 2023-7-31
Ran in:
If your system of differential equations really reads
y1' = y2'
y2 = A/B * t * y1
it follows
y2' = A/B * y1 + A/B * t * y1'
thus
y1' = A/B * y1 / (1- A/B * t)
syms t y1(t)
syms A B real
eqn = diff(y1,t) == A/B * y1 / (1- A/B * t)
eqn(t) = 
y1sol = dsolve(eqn)
y1sol = 
y2sol = A/B * t * y1sol
y2sol = 
diff(y1sol,t)
ans = 
simplify(diff(y2sol,t))
ans = 

更多回答（1 个）

Walter Roberson
Walter Roberson 2023-7-31
Ran in:
tspan = [0 5];
y0 = [0 0.1];
A = 1;
B = 2;
[t,yAB] = ode15s(@(t,y)fun40(t,y,A,B),tspan,y0);
figure
plot(t,yAB)
grid
ylim([-0.01 0.11])
function dyAB = fun40(t,yAB,A,B)
dyAB = zeros(2,1);
dyA(1) = yAB(2);
dyB(2) = (A/B)*t.*yAB(1);
end
  1 个评论
Walter Roberson
Walter Roberson 2023-7-31
Ran in:
syms A B positive
syms y1(t) y2(t)
dy1 = diff(y1);
dy2 = diff(y2);
eqn1 = dy1 == dy2
eqn1(t) = 
eqn2 = y2 == A/B * t * y1
eqn2(t) = 
sol = dsolve([eqn1, eqn2])
Warning: Unable to find symbolic solution.
sol = [ empty sym ]
However, if the derivatives of the two functions are equal then the two functions differ only by a constant, and so you can substitute into
syms C
y1 = y2 + C
y1(t) = 
eqn3 = y2 == A/B * t * y1
eqn3(t) = 
sol = isolate(eqn3, y2)
sol = 
y2 = rhs(sol)
y2 = 
y1 = simplify(y2 + C)
y1 = 
simplify(diff(y1) - diff(y2))
ans = 
0

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