function p_point = ExactSolution(x_point,y_point,t)

% Mach number of the mean flow
M = 0.5;

% parameters of the source term
s_epsilon = 0.5;
s_alpha = log(2)/2;
% position of the source
x_s = 0; y_s = 0;
% angular frequency
omega = (2 * pi) / 30;

% function f(x,y) from the source term
f = @(xi,eta) exp(-s_alpha * ((xi - x_s) .^ 2 + (eta - y_s) .^ 2));

% material derivative of the Green's function
dGdt = @(xi,eta) exp(-1i * (omega * (x_point - xi) * M / (1 - M ^ 2) + omega * t)) .* ((1 + M * M / (1 - M ^ 2)) * besselh(0, omega * sqrt((x_point - xi) .^ 2 + (1 - M ^ 2) * (y_point - eta) .^ 2) / (1 - M ^ 2)) + M * (-1i * (x_point - xi) ./ ((1 - M ^ 2) * sqrt((x_point - xi) .^ 2 + (1 - M ^ 2) * (y_point - eta) .^ 2))) .* besselh(1, omega * sqrt((x_point - xi) .^ 2 + (1 - M ^ 2) * (y_point - eta) .^ 2) / (1 - M ^ 2)));

% product of f(x,y) and dG/dt(x,y,t) as single inline function
func = @(xi,eta) f(xi,eta) .* dGdt(xi,eta);

p_point = real(1i * s_epsilon * (omega / (4 * sqrt(1 - M ^ 2))) * integral2(func,-15,15,-15,15));
% p_point = real(1i * s_epsilon * (omega / (4 * sqrt(1 - M ^ 2))) * integral2(func,-15,15,-15,15,'AbsTol',1e-12,'RelTol',1e-9));

end