I want to write a code for an equation (given in link) but I don't know how can I write double summation sign in MATLAB when one variable goes to infinity and other not. The equation was put forward by Pinder et al 1969 (the paper is attached)
https://latex.codecogs.com/gif.latex?Summ&space;=&space;\sum_{m=1}^{p}\sum_{n=1}^{\infty&space;}(-1)^{n-1}\Delta&space;H.{erfc\frac{2(n-1)u+u\gamma}{2\gamma&space;\sqrt{p-m}}+erfc\frac{2nu-u\gamma}{2\gamma&space;\sqrt{p-m}}&space;}
Of course, I have doubt in your equation. Because the index variable is same for both the summations. You should first check your equation. You may apply Symbolic Mathematics Toolbox. One function which will be useful to you is the function 'symsum'.
http://in.mathworks.com/help/symbolic/symsum.html
Sorry it was typo error. It is m=1:p and n=1:inf. The symbolic tool box can be used for single summation. I tried to use it with for loop for outer summation but useless.
What I am suggesting is:
symsum(symsum,..........))
There are no for loops. This is similar to sum(sum(A)) which gives the summation of all elements of an mXn matrix. You might have tried it. Otherwise, try in this way. Perhaps it will work.
As written, the equation has an error.
I assume, from the first summation (with the sum of delta h_m), that the finite summation (with p as the upper limit) should have index m. Making that interpretation, I assume the rest of the equation is correct and the appearance of distinct n,m is correct. The n sum has the infinite upper limit and creates an oscillating sign.
I also assume you want a numerical answer and programming in MATLAB means you are using numbers and traditional arithmetic to calculate.
Don't use inf for the upper limit, but instead use an adjustable large number (N) to decompose the summation into a lower range (n=1:N) and an upper range (n=N+1:inf).
1. Calculate the lower range finite summation using MATLAB traditional functions (there are a few ways to do summations) and check convergence by setting an acceptable tolerance. The error function compliment has the limits of 0:1 so this should work.
2. The remaining upper range summation (n upper limit to int) is aided by the error function compliment converging to a constant (factor out of the summation). How this is done depends on the other variables (gamma, u, p) compared to N. There may be an envelope in these dimensions defined by the defined tolerance. The remainder could be evaluated using Grandi's series, which is the interesting result of the infinite series 1-1+1-1+1... that is +1/2.
Hi
In general cases, you can follow the instructions in the links below:
http://www.mathworks.com/matlabcentral/newsreader/view_thread/60417
http://www.mathworks.com/help/symbolic/limit.html
Dear Ather Abbas,
Look the link. May be useful.
http://www.ecs.umass.edu/~arwade/courses/fea/matlab_symbolic.pdf
http://ctms.engin.umich.edu/CTMS/index.php?aux=Extras_Plot
Regards, Shafagat
I have written following code;
x = 45; % to calculate omega and u
l = 300; % to calculate omega
p = 100;
omega= x/l; deltaHvec = sin(linspace(0.3,2.6,100));
deltat = 5; % to calculate u
v = 40; % to calculate u
u = x/sqrt(v*deltat); suma = 0;
for i = 1:p
deltaH=deltaHvec(i);
for m = 1:i
for n = 1:1000
e1Arg=(2*(n-1)*u + u*omega) / (2*omega*sqrt(p-m));
e1=erfc(e1Arg);
e2Arg = (2*n*u - u*omega)/(2*omega*sqrt(p-m));
e2 = erfc(e2Arg);
totalerror = e1+e2;
f= (-1)^(n-1) * deltaH * totalerror;
summ(i) = summ(i) + f;
end
end
end
summ;
plot(1:100,summ); hold on; plot(1:100,deltaHvec,'k');
I want to have 100 values of summ i.e One for every different value of 'p' every time using one specific value of 'deltaHvec'. I mean for first first value of 'summ', p=1 and deltaH=deltaHvec(1). For second value of 'summ' 'p=2' and deltaH=deltaHvec(2).
The problem is final graph of 'summ' should be equal or less than amplitude of 'deltaHvec'. But I am getting quite higher values of 'summ' which represents that I am adding extra values in 'summ' with every successive step.
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