TU Wien:Computernumerik VU (Schranz-Kirlinger)/Übungen SS16/Beispiel 34

Lösung

Matlab Code

function Bsp4
x = 0;
xi = [0.01 0.005 0.001 0.0005 0.0001];
y = [0.01*sin(0.01) 0.005*sin(0.005) 0.001*sin(0.001) 0.0005*sin(0.0005) 0.0001*sin(0.0001)];

poly = polyfit(xi,y,4);
der = polyder(poly);

result = polyval(der,x);

fprintf('Result: %0.25f\n', result);

%% einseitiger Differenzenquotient
%%
f = @(x) x*sin(x); 

%%
% h = x1-x0
h = xi(1)-xi(5);
der = (f(xi(5) + h) -f(xi(5)))/h;
fprintf('Result: %0.25f\n', der);

%% zentraler Differenzenquotient
%%
f = @(x) x*sin(x); 

%%
% h = x1-x0
h = xi(1)-xi(5);
der = (f(xi(5) + h) - f(xi(5) - h))/(2*h);
fprintf('Result: %0.25f\n', der);
end