euler polynomial into a matrix form

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Relly Syam 2021-3-27

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Matlab code

hello anyone can help me

I want to find an approximate solution for volterra integral

with truncated euler series with weighted residual method,

in the method I want to find multiple matrices,

I tried with matlab but it doesn't seem to work,

%start
clear;
clc;
syms x t c
n=3;
f(c)=6*c-3*c^2 ;
%determine matrices E and K with collocation point c = {0, 1/3, 1}
c=0;
E=[];
K=[];
for i=1:n;
    E(i)=euler(i,c);
    K(i)=int(euler(i,t),0,c);
end 
E1=E'
K1=K'
F1=f(c)
%c=1/3
c=1/3;
E=[];
K=[];
for i=1:n;
    E(i)=euler(i,c);
    K(i)=int(euler(i,t),0,c);
end 
E2=E'
K2=K'
F2=f(c) 
%c=1
c=1;
E=[];
K=[];
for i=1:n;
    E(i)=euler(i,c);
    K(i)=int(euler(i,t),0,c);
end 
E3=E'
K3=K'
F3=f(c) 
%combine
matrixE=[E1 E2 E3]
matrixK=[K1 K2 K3]
%matrix F
F=[F1 F2 F3]'
%matrix E-K
EK=matrixE-matrixK
%find the coefficient [E-K]X=F => X=inv(E-K)*F
X=inv(EK)*F
%approximate solution
Ua=matrixE*X
%exact solution is u=6*c
%maybe anyone can help me