How to solve coupled partial differential equation with an integral term?
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I want to solve the below given PDE system in MATLAB,
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/414538/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/414543/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/414548/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/414553/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/415823/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/415828/image.png)
I have written a code but I am not able to solve integro differential equation in this system.
%% discretizing a
dx=0.25;
x=0:dx:20;
m=length(x);
% discretizing time
dt=0.01;
%Tp=(10)^(-1);
% Tf=input('enter the max time');
Tf=20;
t=0:dt:Tf;
n=length(t);
%% parameter values
a3=0; a4=1000; rho = 0.2;
c=1; alpha = 0.40; mu = 0.30; k=0.5; lambda=50;
%% size of the matrix
A=zeros(m,n);
B=zeros(m,n);
S=zeros(1,n);
R=zeros(1,n);
sum=zeros(1,n);
%% initial data
S(1) = a4; % S_s
R(1) = a3; % R_s
%% defining functions
for i=1:m
a1(i) = 0; %l_s(a)
a2(i) = 0; %i_s(a)
p(i) = 1700*(1-exp(-x(i))); %p(a)
% p(i) = i; %p(a)
delta1(i) = 0.01; % delta_l(a)
delta2(i) = 0.4; % delta_i(a)
end
%% initial conditions
for i=1:m
A(i,1) = a1(i);
B(i,1) = a2(i);
sum(1)=trapz(p(i).* B(i,1))*dx;
end
% %trapz(p(i)* B(:,i))*dx%
%% discretizing age and time derivative
for j=1:n-1
for i=2:m-1
A(i,j+1)=A(i,j)+dt*(-(A(i+1,j) - A(i-1,j))/(2*dx) - alpha*A(i,j)-delta1(i)*A(i,j));
B(i,j+1)=B(i,j)+dt*(-(B(i+1,j) - B(i-1,j))/(2*dx) +alpha*A(i,j)-delta2(i)*B(i,j));
sum(j+1)=trapz(p(i).* B(i,j))*dx;
S(j+1) = S(j) + dt*(lambda - k*R(j).*S(j) - mu*S(j));
R(j+1) = R(j)+ dt*sum(j+1) - dt*c*R(j);
end
% boundary conditions
A(1,j+1)= rho*k*R(j)*S(j);
B(1,j+1)= (1-rho)*k*R(j)*S(j);
end
plot(t,S,'b-', t,R,'r-');
I have plotted the solution but the plot of R(t) is not correct, I feel that I am not able to solve integro differential correctly. Please help me to solve integro differential equation by some method.
4 Commenti
Bill Greene
il 16 Nov 2020
I am confused by your boundary condition on l. You show
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/415503/image.png)
but it looks like in your code
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/415513/image.png)
Please clarify this.
Risposte (1)
Hewa selman
il 23 Dic 2021
hello it does not work. could you please write the last version of your code again
with regards
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