Daha

%main
%задание 1
a=-pi; b=pi; ns=[5 10 15 20 25 30 35 50 70 100 200 500 1000]; lambda=3/(10*pi);
K=@(x,s) 1./(0.64*cos((x+s)/2).*cos((x+s)/2)-1);
f=@(x) 25-16*sin(x).*sin(x);
u=@(x) 17/2+(128/17)*cos(2*x);
for i=1:length(ns)
    x=linspace(a,b,ns(i));
    h(i)=x(2)-x(1);
    [y,x]=fredII_trapez(K,f,lambda,a,b,ns(i));
    u_=u(x)';
    err(i)=norm(y-u_,inf)/norm(u_,inf);
end
loglog(h,err)
title('loglog(h,err)');
xlabel('h');
ylabel('err');

%задание 2
%main
% a=0; b=1; lambda = 1/2 ;n=1000;
% f=@(x) (5/6)*x;
% K=@(x,s) x*s;
% x=linspace(a,b,n);
% u=@(x) x;
% tic;
% [y,x]=fredII_trapez(K,f,lambda,a,b,n);
% toc;
% % tic;
% % [y,x]=fredII_trapez_upd(K,f,lambda,a,b,n);
% % toc;
% plot(x,y,'ro',x,u(x),'g');
% xlabel('x');
% ylabel('y');
% u_=u(x)';
% err=norm(y-u_,inf)/norm(u_,inf);

для задания 3

function [y,x] = fredII_trapez_upd(K,f,lambda,a,b,n)
x=linspace(a,b,n);
h=x(2)-x(1);
w=[1/2,ones(1,n-2), 1/2]*h*lambda;
%A=-K(x,x')*diag(w')+eye(n);
A=-K(x,x')*spdiags(w',0,n,n)+speye(n);
F=f(x);
y=A\F'
end

% %задание 4
% %main
% a=0; b=1; ns=[5 10 15 20 25 30 50 100]; lambda=-1;
% K=@(x,s) x.*exp(x.*s);
% f=@(x) exp(x);
% for i=1:length(ns)
%     x=linspace(a,b,ns(i));
%     h(i)=x(2)-x(1);
%     [y1,x]=fredII_trapez(K,f,lambda,a,b,ns(i));
%     [y2,x]=fredII_simpson(K,f,lambda,a,b,ns(i));
%     u=@(x) ones(1,numel(x));
%     u_=u(x)';
%     err1(i)=norm(y1-u_,inf)/norm(u_,inf);
%     err2(i)=norm(y2-u_,inf)/norm(u_,inf);
% end
% %plot(h,err1,'r');
% loglog(h,err1,'r')
% hold on
% %plot(h,err2,'g');
% loglog(h,err2,'g')
% title('red - trapez, green - simpson');
% xlabel('h');
% ylabel('err');

function [y,x] = fredII_simpson(K,f,lambda,a,b,n)
x=linspace(a,b,n)';
h=x(2)-x(1);
if mod(n,2)==1
    w=[1/3,2/3*(1+mod(1:(n-2),2)),1/3]*h*lambda;
else
    w=[1/2,5/6,2/3*(1+mod(1:(n-3),2)),1/3]*h*lambda;
end
A=zeros(n);
for i=1:n
    A(:,i)=-w(i)*K(x,x(i));
    A(i,i)=A(i,i)+1;
end
F=f(x);
y=A\F;
end