Solution of Simultaneous Integro-Differential Equation

Hi, I want to solve the intero-differential equation (6) with rest of the equations described from equations 1-9. I am new to this kind of modeling, request to help or suggest how to use MATLAB to solve such model equations.

Thank you.

Sanjib Das Sharma

[Sam Chak]

Hi @Sanjib Das Sharma

According to the PDF, Eq. (6) is the yield distribution function . Though I'm unfamiliar with this model, I'd advise you to type out all equations and paramters (constants) in MATLAB code in the odefcn() function model, like the following Van de Pol example. This allows other people to conveniently test the simulation and correct your code. It's okay even if it does not work.

[t, y] = ode45(@odefcn, [0 20], [2; 0]);

plot(y(:,1), y(:,2)), grid on
title('Limit cycle of Van der Pol oscillator (\mu = 1)');
xlabel('y_{1}'), ylabel('y_{2}')

% Van der Pol oscillator
function dydt = odefcn(t, y)
    % parameter
    mu   = 1;
    
    % ODE in state-space form
    dydt = [y(2);                           % ode dy1/dt for state y1 
            mu*(1 - y(1)^2)*y(2) - y(1)];   % ode dy2/dt for state y2
end

[Torsten]

The way to solve your equations is explained in (10)-(14).