solving an ODE with a constraint equation
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Hi all,
I wondered if there is a numerical solver in MATLAB that can be used to solve this ODE with a constraint:
dy/dx = a/x;
y(0) = 0;
y dx = 1. "y" is a function of "x", and "a" is an unknow constant that also needs to be solved.
It seems that this is a combination of ODE and an nonlinear equation, and is there any way that I can solve both simutaneously? Thank you.
采纳的回答
Torsten
2022-4-1
As you said: You will have to couple a nonlinear solver with an ODE integrator.
I changed the ODE to dy/dx = a*x because of the singularity of your ODE at x=0.
a0 = 1;
a = fzero(@fun,a0)
% Check
res = fun(a)
function res = fun(a)
xstart = 0.0;
xend = 1.0;
fun = @(x,y) [a*x;y(1)];
xspan = [xstart,xend];
y0 = [0;0];
[t,y] = ode45(fun,xspan,y0);
res = y(end,2) - 1.0;
end
更多回答（1 个）
Walter Roberson
2022-4-1
0 个投票
Typically this would be solved as a Boundary Value Problem, such as bvp4c() or bvp5c()
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