clc;clear;tic;
M=5;
N=10;
A=zeros(M+N,M+N);
B=zeros(M+N,1);
F=zeros(M+N,1);
syms x
for i= 1:M
S(i)=pi*i*sym('x');
%fun = @(x) 2.*((diff(sin(S(i)),x)).^2);
result=int(sin(S(i)).^2-((diff(sin(S(i)),x)).^2),0,1);
A(i,i)=result;
end
for i=1:M
for j=M+1:M+N
S(i)=pi*i*sym('x');
D(j)=(j-M)*pi*sym('x');
A(i,j)=int(diff(sin(S(i)),x)*(diff(cos(D(j)),x)),0,1);
end
end
for i=M+1:M+N
for j=1:M
S(j)=(j-M)*pi*sym('x');
D(i)=(i-M)*pi*sym('x');
A(i,j)=int(sin(S(j))*cos(D(i)),0,1);
end
end
for i=M+1:M+N
S(i)=(i-M)*pi*sym('x');
A(i,i)=int(cos(S(i))^2-((diff(cos(S(i)),x))^2),0,1);
end
%define F mtrix(RHS)
for i=1:M
S(i)=i*pi*sym('x');
F(i)=-int(x*sin(S(i)),0,1);
end
B=inv(A)*F;
syms x y
y= @(x) B(1)*sin(pi*x)+B(2)*sin(2*pi*x)+B(3)*sin(3*pi*x)+B(4)*sin(4*pi*x)+B(5)*sin(5*pi*x)+B(6)*cos(6*pi*x)+B(7)*cos(7*pi*x)+B(8)*cos(8*pi*x)+B(9)*cos(9*pi*x)+B(10)*cos(10*pi*x)+B(11)*cos(11*pi*x)+B(12)*cos(12*pi*x)+B(13)*cos(13*pi*x)+B(14)*cos(14*pi*x)+B(15)*cos(15*pi*x);
fplot(y,[0,1]);
