How do I solve complex Integro-Differential equations in MATLAB?

I am somewhat new to solving these kinds of equations but I would like to obtain some graphs/solutions using Analytical method preferebly.

[David Goodmanson]

Hi Aditya,

what variable are you trying to solve this for? Kappa, perhaps?

[Aditya Sreekumar]

Kappa is a constant and the del is varrying btw. But I just need a code example to plot any little complex intergo-diff equations to clear my basics. You can give any example. :)

Answer 1

[Dimitris Kalogiros]

Hi Aditya

In order to solve this kind of equations symbolically, you should have Symbolic Math Toolbox.

Provided that, I'm giving you a tutorial piece of code:

clear all;
clc; close all;

% define symbolic variables
syms r n E w k d 
syms mySum leftTerm

% left term of equation
leftTerm=(r/E)*(w/k)^2

% define term of summation
f=((-1)^(n+1))*(factorial(3)/factorial(2*n+1))*(d^(2*n-2))*(k^(2*n-2))

%calculate sum
mySum=symsum(f , n, 1, inf);
mySum=rewrite(mySum, 'sin')

% substitute variables other than d
rightHand=subs(mySum , k , 1)
leftHand=subs(leftTerm, [r E w k], [1 2 1 1]);

%plot left and right part of equation
fplot(rightHand, [-10 10]); hold on;
fplot(leftHand, [-10 10]); zoom on; grid on;

% numerical solving 
equ= leftHand== rightHand
solNeg=vpasolve(equ, d, [-5 0])
solPos=vpasolve(equ, d, [0 5])

I suggest to run this script within a "Live Script"

At the following picture, you can see the results: