I’m trying to solve this first order ODE problem with initial value solving. I want to plot “a” versus “k”. I want to use initial value problem and root finding method to solve this first order ODE. Please find attached a pdf with an explanation.
I'm trying to solve this problem:
b=a*(1/(a^2*k^2))^0.5; which b is function of a,k
F=(b^6-a^6)*sin(a)*sinh(b)+2*a^3*b^3*cos(a)*cosh(b)-2*a^3*b^3;' which if F is function of b,a
I'm trying to solve this first ordinary equation
da/dk=(-diff(F,b)*diff(b,k))/(diff(F,a)+diff(F,b)*diff(b,a) intiaal value a(0)=14
How can write this problem with MATLAB?
respected Sir,,
I can solve these problems by using ANN. kindly send me the differential equation.
i can guide you how to solve
I attached in pdf file. Please download it from question.
@Zulqurnain Sabir Is it possible to solve Second or higher order ODE (with initial value problem) by using ANN (using MATLAB).
Please send me the procedure (how to solve ODE using ANN).
my email: [email protected]
Thanking you.
You wrote: " b=a*(1/(a^2*k^2))^0.5; which b is function of a,k ."
Is it the right equation? Why not b=1/k ?
Here is a first attempt to get the solution using Maple. A pdf export of a Maple session is enclosed.
It is quick answer that need to be completed to get an accurate solution.
All you need to do is set up functions which evaluate the RHS and use one of the ODE solvers from Matlab. The Matlab Documentation is pretty good at guiding how to set up such programs. As for finding closed form solutions, you may have to do a little algebra to nut a few things out ... have you tried the usual textbook method of finding eigenvalues for the steady state solution? You may also want to check whether those combinations of derivatives wrt F in the denominator may be expressed as a linear function of F (upto some constant factor)., if this is the case then you can rearrange your ODE into something more managable.
If you know that the problem is stiff .. try ODE23 and ODE15s. You may also want to try the ODE suites fully implicit solver (ODE23i I think). Once these are done then try ODE45 and see what is different ... if the differences are huge then you may have look at setting more stringent tolerance and error levels.
You can type at MATLAB prompt >> help ode45 and follow the syntax
with MATLAB ODEsolvers you can also detect events (--> find zeroes), even if I am not sure you need this (see the Maple solution provided some days ago).
Hope this helps!
Season greetings
I am not a Matlab user, but I believe you need a function G(k,a) corresponding to an explicit form of the ODE da/dk = G(k,a(k)) for use with the different solvers as suggested above. Here is a series of Maple instructions to generate the enclosed file "G.m":
> restart;
> b := a(k)/sqrt(1+k^2*a(k)^2):
> F := (b^6-a(k)^6)*sin(a(k))*sinh(b)+2*a(k)^3*b^3*cos(a(k))*cosh(b)-2*a(k)^3*b^3;
> eq := subs(diff(a(k), k) = A, diff(F, k));
> # Second member of ODE in explicit form da/dk = G(k, a(k))
> G := solve(eq, A);
> with(CodeGeneration):
> funG := unapply(subs(a(k) = a, G), [k, a]);
> writeto("G.m");
> Matlab(funG, optimize, resultname = "G");
It is very probably possible to use the Matlab Symbolic Math Toolbox to obtain a similar result, if you or your lab can afford it :-)
Hope this helps! Merry Christmas
I send my answer as a file attachment. Please, answer me. Your sincerely, Anna Tomova.
I send my answer another way as a file attachment too . Please, answer me. Your sincerely, Anna Tomova.
About the question if the solution of ODE a(k), a(0) = 1.8 has zero or not, my answer is: a(k) has'not 0 for every k, because F(0, b(0,k) = 0, but we have proved that if a(0) = 1.8, F (a, b(a, k ) = const = - 116. 051...
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