Invalid indexing for dsolve

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matlab_day 2021-1-12

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https://ww2.mathworks.cn/matlabcentral/answers/715223-invalid-indexing-for-dsolve

评论： Star Strider 2021-1-14

I am trying to make a plot of 2 ODE'S x(t), y(t) with the following code as explained in (https://www.mathworks.com/help/symbolic/solve-a-system-of-differential-equations.html):

syms x(t) y(t)

ode1 = diff(x) == x(t)*y(t) + 0.5*x(t)^3 + x(t)*y(t)^2;

ode2 = diff(y) == -y(t) - 2*x(t)^2 + x(t)^2*y(t);

odes = [ode1; ode2];

cond1 = x(0) == 0;

cond2 = y(0) == 1;

conds = [cond1; cond2];

[xSol(t), ySol(t)] = dsolve(odes,conds);

fplot(xSol)

hold on

fplot(ySol)

grid on

legend('uSol','vSol','Location','best')

However, I ge the following message: "In myODE (line 10)

Error using sym/subsindex (line 857)

Invalid indexing or function definition. Indexing must follow

MATLAB indexing. Function arguments must be symbolic

variables, and function body must be sym expression."

I'm not sure why there is an error since it matches the website I linked above. Thank you!

回答（1 个）

Star Strider 2021-1-12

0
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/715223-invalid-indexing-for-dsolve#answer_596528

在 MATLAB Online 中打开

The equations are nonlinear, and for most nonlinear differential equations, an analytic solution does not exist.

Try this instead:

syms x(t) y(t) T Y 
 
ode1 = diff(x) == x(t)*y(t) + 0.5*x(t)^3 + x(t)*y(t)^2;
ode2 = diff(y) == -y(t) - 2*x(t)^2 + x(t)^2*y(t);
odes = [ode1; ode2];
 
cond1 = x(0) == 0;
cond2 = y(0) == 1;
conds = [cond1; cond2];
[VF,Subs] = odeToVectorField(odes);
ODEfcn = matlabFunction(VF, 'Vars',{T,Y});
[t, Sol] = ode45(ODEfcn, [0 1], [1 0]+eps);
figure
yyaxis left
plot(t, Sol(:,1))
yyaxis right
plot(t, Sol(:,2))
grid on
legend(string(Subs),'Location','N')

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matlab_day 2021-1-14

Thank you. I changed the initial conditions so that I would have x(0) = -5, -.4,...,.4, .5, and I wanted my interval for my independent variable to be from 0 to 10. When I used the following code:

comb_func = @(t,x)[x(1)*x(2) + 0.5*x(1)^3 + x(1)*x(2)^2; -x(2) - 2*x(1)^2 + x(1)^2*x(2)]; %System of ODES x(t) = x(1), y(t) = x(2)

tspan = [0 10]; % Choose Time Vector

for k = 1:11

ic = -.5 + k*.1; % Set Initial Conditions

[tc{k}, Sol{k}] = ode45(comb_func, tspan, ic); % Integrate & Store Results

end

it spit the error message

Index exceeds the number of array elements (1).

Error in myODE>@(t,x)[x(1)*x(2)+0.5*x(1)^3+x(1)*x(2)^2;-x(2)-2*x(1)^2+x(1)^2*x(2)]

(line 16)

which is weird because this error message doesn't appear when I change nothing else but replace the initial conditions line to the random number generator you had.

Star Strider 2021-1-14

在 MATLAB Online 中打开

You have 2 differential equations, so you need 2 initial conditions.

Try this:

ic = [-.5,  k*0.1];                                            % Set Initial Conditions

That will not throw the same error, however you could still encounter the warning about an infinite result. (I did not test the integration code with those initial conditions, so I cannot determine that.)

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