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Solving of integro-differential equation

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Illya Khromov
Illya Khromov on 3 Sep 2015
How one can solve numerically using MatLab the second order integro-differential equation of the type y''-a*integral(f(t-t1)*y'*dt1)-b*y=0 ? Any suggestions are highly appreciated. Thanks in advance.

Answers (1)

Claudio Gelmi
Claudio Gelmi on 7 Jan 2017
Edited: Claudio Gelmi on 30 Jan 2017
Hi, try using this solver developed in MATLAB:
"IDSOLVER: A general purpose solver for nth-order integro-differential equations": http://dx.doi.org/10.1016/j.cpc.2013.09.008
MATLAB solver here for download (free): http://cpc.cs.qub.ac.uk/summaries/AEQU_v1_0.html
Best wishes,
Claudio
  2 Comments
Mohan Aditya Sabbineni
Mohan Aditya Sabbineni on 25 Jun 2019
Please help me in solving this integro differential equation. I am unable write a code for this.
∂f/∂t(H(f)(f/∂x)=0
where [H(f)] is hilbert transform of 'f.'
and f=f(x,t) and initial condition is f(x,0)=cos(x) and also has periodic boundary conditions given by F{H{f(x′,t)}}=i⋅sgn(k)F{f(x,t)}, where F(f(x,t) is fourier transform of f(x,t).
and here ''t'' runs from 0 to 1.3 seconds
so I think we have to use iterations on basis of 't' while solving this equation.
And suggestions are highly appreciated.

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