Solving Integro-differential equation with limited integral
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Hi,
How can I solve this equation numerically using matlab
w''''=w''*int(w'^2,0,1)
I tried using the standard form of ODE function, the only problem I faced is how to represent that limited integral Thanks
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Torsten
le 25 Juin 2015
Write your integro-differential equation as
w1'=w2
w2'=w3
w3'=w4
w4'=w3*integral_{t=0}^{t=1}w2^2(t') dt'
Then discretize the interval [0:1] in n subintervals 0=t(1)<t(2)<...<t(n)=1.
Compute the derivatives as
wj'(t(i))=(wj(t(i+1))-wj(t(i)))/dt (j=1,2,3,4)
and compute the integral using the trapezoidal rule.
You'll arrive at a polynomial system (order 3) of equations for the unknowns
wj(t(2)),wj(t(3)),...,wj(t(n)) (j=1,2,3,4)
which can be solved by fsolve, e.g.
No chance to use ODE45 in this case.
Another way might be to use ODE45 and iteratively adjust the value of the integral, but I'm not sure whether this method will converge.
Good luck !
Best wishes
Torsten.
1 commentaire
Hewa selman
le 22 Déc 2021
Hello
Now are you sure that we can adjust the value of integral, then put it in system and solve it by ode45 or ode15s.
Plus de réponses (2)
Claudio Gelmi
le 6 Jan 2017
Take a look at this solver:
Article "IDSOLVER: A general purpose solver for nth-order integro-differential equations": http://dx.doi.org/10.1016/j.cpc.2013.09.008
Best wishes,
Claudio
2 commentaires
Fernando Fernandes
le 14 Jan 2021
I've downloaded your paper, but i'm a beginner in Matlab. Do I need the solver in http://cpc.cs.qub.ac.uk/summaries/AEQU_v1_0.html ???
How can I install this?
ash
le 28 Juin 2015
4 commentaires
Torsten
le 30 Juin 2015
Sorry, should read
(w4(t(i+1))-w4(t(i)))/h = [sum_{j=1}^{j=Npnts-1}(w2(t(j+1))+w2(t(j)))*h/2]*w3(t(i))
Best wishes
Torsten.
SOZHAESWARI P
le 5 Sep 2021
How to solve the numerical solution of nonlinear parabolic integro differential equation for two grid finite element method example MATLAB codings
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