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Comment: Migrated to Confluence 5.3

 

 

a) og b) og c)

 

 

Code Block
languagenone
function result = simpsons(a,b,Nn,f)
N = N+isEven(N)-1;
h = calcDelta(a,b,N);
result = h/3*f(h*0);
mult = [4,2];
for i = 1:N-1
    result = result +  h/3*f(h*i)*mult(mod(i,2)+1);
end
result = result + h/3*f(h*N);
end
function even = isEven(n)
even = mod(n,2)+1;
end

function h = calcDelta(a,b,n)
h = (b-a)/n    if mod(n, 2) ~= 0
        error('Parameteren n må være et partall, var %d\n', n);
    end
    dx = (b-a)/n; 
    y= f(a:dx:b);
    yodd = 2*sum(y(3:2:n-1));
    yeven = 4*sum(y(2:2:n));
    ysum = y(1) + yodd + yeven + y(n+1);
    result = dx/3 * ysum;
end

 

b)

Code Block
languagenone
function result = simpsons_error(start, stop, error, fn)
N = 2; % N må være et partall
Si = simpsons(start, stop, N, fn);
S2i = simpsons(start, stop, 2*N, fn);
while abs(Si-S2i) >= error
    N = 2 * N;
    Si = S2i;
    S2i = simpsons(start, stop, 2*N, fn);
end
fprintf('Antal ledd: %d\n', N);
result = Si;
end