In [3]:
x_e = linspace(0,2); 
C1 = exp(-4)/(1+exp(-4)); C2 = C1*exp(4);
f_e = C1*exp(x_e) + C2*exp(-x_e);
plot(x_e, f_e); xlabel("x"); ylabel("f(x)");
In [2]:
pkg load odepkg;
In [11]:
fun  = @(x,y) [ y(2); y(1) ];

bc  = @(ya, yb) [ya(1)-1; yb(2)];

xd = linspace(0, 2, 10);
ya = zeros(2, length(xd));

solinit.x = xd; solinit.y=ya;

res = bvp4c(fun, bc, solinit);
In [15]:
plot(res.x, res.y(1,:), "-;f(x);",res.x, res.yp(1,:), "-;f'(x);");  hold on; line(xlim, [0 0]); hold off;
In [17]:
fun  = @(x,y) [ y(2); 2*y(1)-2*y(2)-3];

bc  = @(ya, yb) [ya(1)-1; yb(1)+2];

xd = linspace(0, 2, 10);
ya = zeros(2, length(xd));

solinit.x = xd; solinit.y=ya;

res = bvp4c(fun, bc, solinit);

AbsErr =  0.94892
RelErr =  0.059077
Nint =  18
AbsErr =  0.42276
RelErr =  0.014300
Nint =  36
AbsErr =  0.19801
RelErr =  0.0035005
Nint =  72
AbsErr =  0.095601
RelErr =  0.00086465
In [21]:
plot(res.x, res.y(1,:), "-;f(x);",res.x, res.yp(1,:), "-;f'(x);");  hold on; line(xlim, [0 0]); hold off;