So you have a constant source term
int^1_0(y'*x)dx
in all grid points - independent of the position x in the interval [0 1] ?
Then use
x = linspace(0,1,100);
solinit = bvpinit(x,[2 4]);
source = 0;
tol = 1e-3;
error = 1.0;
while error > tol
sol = bvp4c(@(x,y)ode2(x,y,source),@bc2,solinit);% ВЫЗЫВАЕМ СОЛВЕР BVP4C:
source_new = trapz(sol.x,sol.x.*sol.y(2,:));
error = abs(source_new - source);
source = source_new;
end
plot(sol.x,sol.y(1,:));
grid on
legend('y(t)');
xlabel('t');
function dy = ode2(x,y,source)%y''+y'=1+int^1_0(y'*x)dx;y(0) = 2;y(1) = 4;
dy = zeros(2,1); % создает нулевой вектор-столбец
dy(1)=y(2);
dy(2)=1-y(2)+source;
end
function res = bc2(ya,yb)
res = [ya(1)-2
yb(1)-4];
end
