Please, I am new in MATLAB and need some help as to whether MATLAB can perform this integration, and how to go about it. I have tried 'quad', 'quad8', 'trapz' and even a sum approach but it returns either a not-a-number answer or mtimes error or mrdivide error message. What I want to do is this (Pressure response of a horizontal observation well at a distance xd, yd and zd from a producer)(adsbygoogle = window.adsbygoogle || []).push({});

integral= (1/(sqrt(td)))*(exp(yd^2/(4*td)))*(erf((1+xd)/(2*sqrt(td)))+erf((1-xd)/(2*sqrt(td))))*(1+2*(exp((-n^2*pi^2*td)/hd^2)*cos(n*pi*zwd)*cos(n*pi*((zd/hd)+zwd))));

xd, yd, zd, hd and zwd are constants.

i am integrating from 0 to td for td values of 0.001 to 10000

for each of the integral segment, 0.001 to 10000, (exp((-n^2*pi^2*td)/hd^2)*cos(n*pi*zwd)*cos(n*pi*((zd/hd)+zwd))) will be summed for n=1 to infinity. ie Ʃ(exp((-n^2*pi^2*td)/hd^2)*cos(n*pi*zwd)*cos(n*pi*((zd/hd)+zwd))) for n=1 to ∞

This is my recent attempt: where I did td =1 to 10000; and n= 1 to 100 just for it to work first.

----------------------

clc

x=2800;

y=0;

z=50;

zw=50.165;

kx=300;

ky=300;

kz=100;

l=1000; %well half length

h=100;

% t=150;

% td=(0.0002637*ky*t)/(phi*mu*ct*xf.^2)

k=nthroot(kx*ky*kz,3);

xd = x/l*sqrt(k/kx);

yd = y/l*sqrt(k/ky);

zd = z/h;

zwd=zw/h;

hd = h/l*sqrt(k/kz);

for i = 1:1e+1:10000

for j=1:100

int(i,j)= (1./(sqrt(td(i)))).*(exp(yd.^2./(4.*td(i)))).*(erf((1+xd)./(2.*sqrt(td(i))))+erf((1-xd)./(2.*sqrt(td(i))))).*(1+2.*(exp((-n(j)^2.*pi^2.*td(i))./hd.^2).*cos(n(j)*pi*zwd).*cos(n(j)*pi*((zd./hd)+zwd))));

end

end

p=sum(int*10,3)

Error: ??? Undefined function or method 'td' for input arguments of type 'double'.

**The attached document contains the equation.

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# Long Numerical Integration: Is this possible with MATLAB?

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