how to describe the nth term of convolution in matlab

how I can describe , I need this code in the applicatin of differential transformation method

[Wasim Abbas]

I have two functions u and v, and I know and

Answer 1

[Ameer Hamza]

See conv(): https://www.mathworks.com/help/matlab/ref/conv.html. You need to provide the complete array of u and v for convolution.

[Wasim Abbas]

clear all

S(1) = 790;

I(1) = 10;

R(1)= 0;

N = S(1) +I(1) + R(1);

beta= 1 / 2;

gamma = 1 / 3;

h = 1;

t(1) =0;

nstop=100; %the total number of iteration

fom.x(1)=S;

fom.y(1)=I;

fom.z(1)=R;

for i = 1 :nstop

[dS,dI,dR]=func2(fom.x(i),fom.y(i),fom.z(i),N,beta,gamma);

for j=1:100

syms i j

k(i)= symsum(fom.x(i)*fom.y(j-i));

end

fom.x(i+1)= -(beta/N)*k(i);

fom.y(i+1)= (beta/N)*(k(i))-gamma*fom.y(i);

fom.z(i+1) = gamma*fom.y(i);

end

[Wasim Abbas]

this is my function

function [dS,dI,dR] =func2(S,I,R,N,b,g)

dS=(-b* S * I/N);

dI=(b* S * I /N) - g*I;

dR= g*I;

end

[Wasim Abbas]

I tried to use conv() as well, but it does not work or may be I can't use it acurately.

[Ameer Hamza]

Can you provide the actual statement of your problem in mathematical form? How u and v are defined?

[Wasim Abbas]

DS in above coment is u and DI is v initial conditions are describe in my code

[Wasim Abbas]

This picture shows the slotion of system of equations.

[Wasim Abbas]

In 1st and second equation I need some help to describe summations.

[Ameer Hamza]

I don't think you need conv() here. If you have S and I vector of size k+1, then you can just use

sum(S.*I(end:-1:1))

to calculate this term.