Solving an integral equation
3 Ansichten (letzte 30 Tage)
Ältere Kommentare anzeigen
Kaz Middelhoek
am 3 Jun. 2021
Kommentiert: Bjorn Gustavsson
am 3 Jun. 2021
I'm looking to implement a solution to the following equation:
, where a is a known constant, for demonstration purposes set to 5 below.
Code that I tried:
syms r(t)
i=int(1/(r.^4),0,t)
solve(r==(1-5*i),r)
No clue how to tackle the problem. Thanks in advance!
0 Kommentare
Akzeptierte Antwort
Bjorn Gustavsson
am 3 Jun. 2021
For this I think pen-and-paper might be easier than using the symbolic toolbox. Simply differentiate both sides of your definition of r and convert your integral equation into a differential equation:
This simplifies to (at least for some nice-constraints on r):
That way you now have a reasonably ordinary ODE instead. This is most hand-wavy lacking mathematical rigor, but you should be able to add that if required.
HTH
2 Kommentare
Bjorn Gustavsson
am 3 Jun. 2021
You're welcome. This is the standard way (I've been taught) of attacking this type of integral equations, for others you might start to look at the methods for solving integral equations in chebfun.
Weitere Antworten (0)
Siehe auch
Kategorien
Mehr zu Ordinary Differential Equations finden Sie in Help Center und File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!