Direct Quadrature for Delay Renewal Equation

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Muhammad 2024년 10월 23일

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https://kr.mathworks.com/matlabcentral/answers/2161585-direct-quadrature-for-delay-renewal-equation

댓글: Muhammad 2024년 10월 23일

I'm trying to solve a delay renewal equation with a quadratic nonlinearity using direct quadrature in MATLAB. Here's the code I'm using, but I'm not getting the expected results. Can someone help me identify any mistakes or suggest improvements?

gamma = 5; 
tau = 3;   
t_min = 0; 
t_max = 20; 
dt = 0.1; 
t_vals = t_min:dt:t_max; 
phi = @(t) 0.5 * ones(size(t));  
x_vals = zeros(size(t_vals));
x_vals(1) = phi(0);  
for i = 2:length(t_vals)
    t = t_vals(i);
    integral_term = integral(@(theta) delayed(t + theta, t_vals, x_vals, phi) ...
        .* (1 - delayed(t + theta, t_vals, x_vals, phi)), -tau, -1, ...
        'RelTol', 1e-10, 'AbsTol', 1e-10);
    x_vals(i) = (gamma / 2) * integral_term;
end
figure;
plot(t_vals, x_vals, 'LineWidth', 2);
xlabel('Time');
ylabel('x(t)');
title('Solution of the Delay Renewal Equation (Direct Quadrature)');
function val = delayed(t, t_vals, x_vals, phi)
if t < 0
    val = phi(t);  
else
    val = interp1(t_vals, x_vals, t, 'linear', 'extrap');  
end
end

Thanks in advance

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Sahas 2024년 10월 23일

Hi,

Can you share the expected results? It will help me assist you better.

Muhammad 2024년 10월 23일

MATLAB Online에서 열기

like here for different gamma values, different results but for my code it is not possible

gamma = 0.5;

tau = 3;

t_min = 0;

t_max = 20;

dt = 0.1;

t_vals = t_min:dt:t_max;

phi = @(t) 0.5 * ones(size(t));

x_vals = zeros(size(t_vals));

x_vals(1) = phi(0);

for i = 2:length(t_vals)

t = t_vals(i);

integral_term = integral(@(theta) delayed(t + theta, t_vals, x_vals, phi) ...

.* (1 - delayed(t + theta, t_vals, x_vals, phi)), -tau, -1, ...

'RelTol', 1e-10, 'AbsTol', 1e-10);

x_vals(i) = (gamma / 2) * integral_term;

end

Warning: Inf or NaN value encountered.

figure;

plot(t_vals, x_vals, 'LineWidth', 2);

xlabel('Time');

ylabel('x(t)');

title('Solution of the Delay Renewal Equation (Direct Quadrature)');

function val = delayed(t, t_vals, x_vals, phi)

if t < 0

val = phi(t);

else

val = interp1(t_vals, x_vals, t, 'linear', 'extrap');

end

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Direct Quadrature for Delay Renewal Equation

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Direct Quadrature for Delay Renewal Equation

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