also does anyone know why, my 3/8 rule is different to the one on the net??? mine is h/8(f0+3f1+3f2+f3) and theirs is 3h/8(f0+3f1+3f2+f3) and my code works and is right according to matlab's inbuilt besselj function?
hi this is my code
can anyone fix it for me, to include the error... i got it right without it, but for some reason putting the error in, stuffs it up, and cant find whereCode:function [y]=BJ(n,x) N=100; b=pi; a=0; h=(b-a)/N; % Remeber that y(1) is the first element, not y(0). S=0; for i=0:N-1 tj=i*h; delta=a:b; y(1)=cos((n*tj)-x*sin(tj)); y(2)=cos((n*(tj+h/3))-x*sin(tj+h/3)); y(3)=cos((n*(tj+(2*h/3)))-x*sin(tj+(2*h/3))); y(4)=cos((n*(tj+h))-x*sin(tj+h)); y4(delta)=((x^4)*((cos(delta))^4)-4*n*(x^3)*((cos(delta))^3)+(4+6*(n^2))*(x^2)*((cos(delta))^2)-4*x*n*(1+(n^2))*cos(delta)+(n^4)-3*(x^2)*((sin(delta))^2))*cos(n*delta-x*sin(delta))+6*sin(n*delta- x*sin(delta))*((n^2)-2*x*cos(delta)*n+(x^2)*((cos(delta))^2)+(1/6))*x*sin(delta); S = S+((h/8)*y(1))+((3*h/8)*y(2))+((3*h/8)*y(3))+((h/8)*y(4))-((3*(h^5)/80)*(y4(delta))); end y=1/pi*S; end
it says something about the matrix must be square????
here's the original qn
Let us consider an approximation to an integral. Let f(x) be some continuous function on
[a, b]. We wish to find an approximation for the integral
I = int from a to b of f(x)dx
in the following manner:
Subdivide the interval into N intervals of length h = (b−a)/N. Let xi = ih for i = 0, . . . ,N.
Let
Ij = int from 0 to h of f(xj+t)dt
Find a cubic polynomial Pj (x) that goes through (xj , f(xj)), (xj + h/3,f(xj + h/3)),(xj+2h/3, f(xj+2h/3) and (xj+1,f(xj+1))
We form an approximation for the integral by letting
I=sum(j=0 to N-1) of w0*f(xj)+w1*f(xj+h/3)+w2*f(xj+2h/3)+w3*f(xj+1)
Find these weights, wi.
In 2 peices of code, plot the first three Bessel functions, J0(x), J1(x) and J2(x), on the
interval [0, 20]. The first peice of code should be a MATLAB function BJ(x, n) outputing
the approximation for the integral representation of Jn, given by
Jn(x) =(1/pi)int from 0 to pi of cos(nt − x sin t)dt
using the above method for 100 subdivisions of [0, pi]. The second peice of code should call
the function an produce the required plots with 2000 subdivisions of [0, 20].
I dont need to find the error for qn, but i was just curious, on how you would do it? does it even matter?