Beispiel - SAM - ETH Zürich

5 % Implicit Euler
6 y_imp = y0; y = y0;
7 f o r k=1:N
8 % Implicit Euler equation for next angle
9 F = @(x) x+h*h*g/l*sin(x) - y(1) - h*y(2);
0 [y(1),Fval] = fsolve(F,y(1)+h*y(2)); % solve non-linear system of
equations
1 f p r i n t f(’Impl Euler step %d: residual %f\n’,k,Fval);
2 y(2) = y(2) - h*g/l*sin(y(1));
3 y_imp = [y_imp,y];
4 end
5
6 % Implicit midpoint rule
7 y_mid = y0; y = y0;
8 rhs = @(y) [y(2);-g/l*sin(y(1))];
9
0 f o r k=1:N
1 % Implicit equation (1.4.19) for implicit midpoint rule
2 F = @(x) (x - h*rhs(y+0.5*x));
3 [dy,Fval] = fsolve(F,h*rhs(y)); y = y+dy;
4 f p r i n t f(’Impl midp step %d: residual %f\n’,k,norm(Fval));
5 y_mid = [y_mid,y];
6 end
7
Numerische
Mathemtik
R. Hiptmair
rev 35327,
25. April
2011
1.4
p. 91