How to solve coupled partial differential equation with an integral term?
2 visualizaciones (últimos 30 días)
Mostrar comentarios más antiguos
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 comentarios
Bill Greene
el 16 de Nov. de 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.
Respuestas (1)
Hewa selman
el 23 de Dic. de 2021
hello it does not work. could you please write the last version of your code again
with regards
0 comentarios
Ver también
Categorías
Más información sobre Boundary Conditions en Help Center y File Exchange.
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!