set(0, "defaultlinelinewidth", 5);
set (0, "defaulttextfontname", "TimesNewRoman")
set (0, "defaulttextfontsize", 20)
set (0, "DefaultAxesFontName", "TimesNewRoman")
set(0, 'DefaultAxesFontSize', 20)
x = linspace(0, 1, 100);
xe = linspace(0, 1, 6);
ep = 0.1;
m1 = (-1 + (1+ep).^0.5)/ep; m2 = (-1 - (1+ep).^0.5)/ep; A = 1/(exp(m1) - exp(m2)); B = -A;
ye = A*exp(m1*xe) + B*exp(m2*xe);
plot(xe, ye,"-;Exact;", "marker","s"); xlabel('x'); ylabel('y(x)');
hold on;
yo0 = exp((x-1)/2); yo1 = 1/2*(1-x).*exp((x-1)/2);
yo = yo0 + ep*yo1;
plot(x, yo,"-;Outer sol;","linestyle","--");
yi = exp(-1/2)*(1-exp(-2*x/ep));
plot(x, yi, "-;Inner sol;","linestyle","--");
pkg load odepkg;
function dydx= fun(x,y)
ep = 0.1;
dydx = [y(2); -2*y(2)/ep+y(1)/ep];
end
function ye=bc(ya, yb)
ye = [ya(1)-0.0; yb(1)-1.0];
end
xi = linspace(0, 1, 10);
ya = zeros(2, length(xi));
solinit.x = xi; solinit.y=ya;
res = bvp4c(@(x,y)fun(x,y), @(x,y)bc(x,y), solinit);
plot(res.x, res.y(1,:),"-;Using odepkg;","linestyle", '-.');
legend();
hold off;
warning: function D:\Octave-5.2.0\mingw64\share\octave\packages\odepkg-0.8.5\ode23.m shadows a core library function warning: called from load_packages_and_dependencies at line 48 column 5 load_packages at line 47 column 3 pkg at line 461 column 7 warning: function D:\Octave-5.2.0\mingw64\share\octave\packages\odepkg-0.8.5\ode45.m shadows a core library function warning: called from load_packages_and_dependencies at line 48 column 5 load_packages at line 47 column 3 pkg at line 461 column 7 warning: function D:\Octave-5.2.0\mingw64\share\octave\packages\odepkg-0.8.5\odeget.m shadows a core library function warning: called from load_packages_and_dependencies at line 48 column 5 load_packages at line 47 column 3 pkg at line 461 column 7 warning: function D:\Octave-5.2.0\mingw64\share\octave\packages\odepkg-0.8.5\odeplot.m shadows a core library function warning: called from load_packages_and_dependencies at line 48 column 5 load_packages at line 47 column 3 pkg at line 461 column 7 warning: function D:\Octave-5.2.0\mingw64\share\octave\packages\odepkg-0.8.5\odeset.m shadows a core library function warning: called from load_packages_and_dependencies at line 48 column 5 load_packages at line 47 column 3 pkg at line 461 column 7