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

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Aditya Sreekumar
Aditya Sreekumar 2018-8-6
编辑： Dimitris Kalogiros 2018-8-10
I am somewhat new to solving these kinds of equations but I would like to obtain some graphs/solutions using Analytical method preferebly.
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Aditya Sreekumar
Aditya Sreekumar 2018-8-9
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. :)

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Dimitris Kalogiros
编辑：Dimitris Kalogiros 2018-8-10
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:

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