SanT Solution function S=cotes(f,a,b,N,nodes) %programnewtoncotesrule.m Newton-C

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function S=cotes(f,a,b,N,nodes) %programnewtoncotesrule.m Newton-Cotes numerical integration . % % Inputs: % % f - function to be integrated % a - lower limit of integration % b - upper limit of integration % N - Requested number of grid points % nodes - number of nodes in Newton-Cotes formula % % Sample Usage: % % >>cotes(@sin,0,pi/2,20,5) % % ans = % 0.999999999501637 % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% N=(nodes-1)*ceil(N/(nodes-1)); N1=N+1; x=linspace(a,b,N1)'; h=x(2)-x(1); g=f(x); endpts=g(1)+g(N1); switch nodes case{2} % Trapezoidal Rule Q=(h/2)*(endpts+2*sum(g(2:N))); case{3} % Simpson's Rule Q=(h/3)*(endpts+4*sum(g(2:2:N))+2*sum(g(3:2:N))); case{4} % Simpson's 3/8 Rule Q=(3*h/8)*(endpts+3*sum(g(2:3:N)+g(3:3:N))+2*sum(g(4:3:N))); case{5} % Boole's 4/90 Rule Q=(4*h/90)*(7*endpts+32*sum(g(2:4:N))+... 12*sum(g(3:4:N))+32*sum(g(4:4:N))+14*sum(g(5:4:N))); case{6} Q=(5*h/288)*(19*endpts+75*sum(g(2:5:N)+g(5:5:N))+... 50*sum(g(3:5:N)+g(4:5:N))+38*sum(g(6:5:N))); case{7} Q=(6*h/840)*(41*endpts+216*sum(g(2:6:N)+g(6:6:N))+... 27*sum(g(3:6:N)+g(5:6:N))+272*sum(g(4:6:N))+... +82*sum(g(7:6:N))); case{8} Q=(7*h/17280)*(751*endpts+3577*sum(g(2:7:N)+g(7:7:N))+... 1323*sum(g(3:7:N)+g(6:7:N))+2989*sum(g(4:7:N)+g(5:7:N))+... +1502*sum(g(8:7:N))); case{9} Q=(4*h/14175)*(989*endpts+5888*sum(g(2:8:N)+g(8:8:N))-... 928*sum(g(3:8:N)+g(7:8:N))+10496*sum(g(4:8:N)+g(6:8:N))-... 4540*sum(g(5:8:N))+1978*sum(g(9:8:N))); case{10} Q=(9*h/89600)*(2857*endpts+15741*sum(g(2:9:N)+g(9:9:N))+... 1080*sum(g(3:9:N)+g(8:9:N))+19344*sum(g(4:9:N)+g(7:9:N))+... 5778*sum(g(5:9:N)+g(6:9:N))+5714*sum(g(10:9:N))); case{11} Q=(5*h/299376)*(16067*endpts+106300*sum(g(2:10:N)+g(10:10:N))-... 48525*sum(g(3:10:N)+g(9:10:N))+272400*sum(g(4:10:N)+g(8:10:N))-... 260550*sum(g(5:10:N)+g(7:10:N))+427368*sum(g(6:10:N))+... 32134*sum(g(11:10:N))); otherwise error('Order must be between 2 and 11'); end

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