higher order polynomial expression

I want to implement matlab code for set of 11 polynomials expression and upto 3rd order derivatives. I want to solve this equation with intergration of all 11 set of polynomials. eg. K = intergration with limit 0 to 1 (ai(x) bj(x) dx), where i = 0 and j = 0 to 11

I have created this:

%Some  Polynomials defined over the interval[0,1]

i want this as ai(x) and i = 0 means N0 should be selected

N0 =  [0 0 0 0 0 0 0 0 0 0 1 -1 0];
N1 =  [0 0 0 0 0 0 0 0 0 1 -1 0 0];
N2 =     [0 0 0 0 0 0 0 0 1 -1 -1 1 0];
N3  =    [0 0 0 0 0 0 0 1 -1 -3 0 3 0];
N4   =   [0 0 0 0 0 0 1 -1 -6 6 3 -3 0];
N5    =  [0 0 0 0 0 1 -1 -10 10 15 -15 0 0];
N6    =  [0 0 0 0 1 -1 -15 15 45 -45 -15 15 0];
N7   =   [0 0 0 1 -1 -21 21 105 -105 -105 105 0 0];
N8  =    [0 0 1 -1 -28 28 210 -210 -420 420 105 -105 0];
N9   =   [1 -10 -36 36 378 -378 -1260 1260 1260 945 -945 0 0];
N10   =   [1 -1 -45 45 630 -630 -3150 3150 4725 -4725 -945 945 0];

%1st order

for bj(x) this 1st order should be selected in an integration. and j = 0 to 11 means N01 to N101

N01= polyder (N0)
N11= polyder (N1);
N21= polyder (N2);
N31= polyder (N3);
N41= polyder (N4);
N51= polyder (N5);
N61= polyder (N6);
N71= polyder (N7);
N81= polyder (N8);
N91= polyder (N9);
N101= polyder (N10);

in above first order size of row vector is also changes

please help me with this code.

Thank you in advance!

[John D'Errico]

Hint: this is why you don't create numbered variables as you want to do. MATLAB is not a spreadsheet. It does not work well as a spreadsheet, though people seem to love to try exactly that.

Instead, learn to create vectors and arrays. Learn about cell arrays, although in this case, a simple matrix seems like it would be sufficient, since you seem to have a rectangular array of polynomial coefficients.

That you want to compute up to the third derivative of high order polynomials is a dangerous thing, probably leading to numerical garbage as a result. But what can I say there? People do all sorts of things I think strange. Your choice.

One last point - the word is integration, not intergration. A pretty minor point, I'll admit.

[TAGNE NOUMBISSI ROMUALD]

Hello Hirenkumar Tailor and John D'Errico

I would like in the measure of the possible to have an example of code on the numerical asymptotic method treating the problems of nonlinearity in physics (method based on the assumption of the unknowns like a series of development of Taylor) as similarly treats your code here- above

thank you in advance

thanks

[Hirenkumar Tailor]

John D'Errico sir, can you give me sample or example of cell array for polynomials? And if i will take derivation of that polynomials, size of row vector is reduced, how to keep it same? Yes it was spelling mistake, but how to take integration of those cell arrays?

I have gone through convolution for polynomials and also read about polyint which supports only two variables, Here I have 11 polynomials.

Please help me with code.

[Hirenkumar Tailor]

Thanks John D'Errico sir

I have modified my code as this:

N = {[0 0 0 0 0 0 0 0 0 0 1 -1 0], [0 0 0 0 0 0 0 0 0 1 -1 0 0], [0 0 0 0 0 0 0 0 1 -1 -1 1 0], [0 0 0 0 0 0 0 1 -1 -3 0 3 0], [0 0 0 0 0 0 1 -1 -6 6 3 -3 0], [0 0 0 0 0 1 -1 -10 10 15 -15 0 0], [0 0 0 0 1 -1 -15 15 45 -45 -15 15 0], [0 0 0 1 -1 -21 21 105 -105 -105 105 0 0], [0 0 1 -1 -28 28 210 -210 -420 420 105 -105 0], [1 -10 -36 36 378 -378 -1260 1260 1260 945 -945 0 0], [1 -1 -45 45 630 -630 -3150 3150 4725 -4725 -945 945 0]}

for i=1:11

N1(i) = { polyder(N{1,i}) }

end

for j=1:11

N2(j) = { polyder(N1{1,j}) }

end

for k=1:11

N3(k) = { polyder(N2{1,k}) }

end

now problem is, if I derivate N, then N1, N2, N3 does not produce same size of vector, i.e 1x13. How to do that? and also put some more light on integration of all this polynomials.