Do all of yangtheary's problems come from a list of problems posed by Robert Israel? Is yangtheary Robert Israel in disguise?

@Bendesarts I don't know about exporting it,

@Bendesarts I don't know about exporting it,

@abbeykabir Thank you for the kind words.

Sorry, I have no idea what "error analysis" means with respect to this problem.

I noticed something about the way you set the values of the x[i] that seemed strange. This might be the source of your problem. You have

x[i]:= x[i-1] + i*h

I think that should be either (both the below are equivalent)

x[i]:= x[0] + i*h

or

x[i]:= x[i-1] + h

You are essentially doing both of the above, with the result that your x[i] are not evenly spaced (and that seems strange to me).

You are right about seq, but not every for loop can be replaced by seq.

First check out what I said about the x[i]'s, then I'll show you how to replace your for loop.

@abbeykabir Thank you for the kind words.

Sorry, I have no idea what "error analysis" means with respect to this problem.

I noticed something about the way you set the values of the x[i] that seemed strange. This might be the source of your problem. You have

x[i]:= x[i-1] + i*h

I think that should be either (both the below are equivalent)

x[i]:= x[0] + i*h

or

x[i]:= x[i-1] + h

You are essentially doing both of the above, with the result that your x[i] are not evenly spaced (and that seems strange to me).

You are right about seq, but not every for loop can be replaced by seq.

First check out what I said about the x[i]'s, then I'll show you how to replace your for loop.

@Alex Smith : If you don't like the 2d input, why don't you just make 1d Maple Input the default?

I agree with you about the pedagogical value of the Maple Input syntax.

@henryabiola Does your matrix contain n[s] in element a11? Or should that be eta[s] as in element a22?

Also, note that you mislabelled element a56 as a66.

@mehdi jafari 

Let S(d) = sum(p(k), k= 1..10^d-1)

(so S(2) = p(1) + ... + p(99), for example).

Then S(d) satisfies the recurrence

S(d) = 46*(S(d-1) + 1) - 1, S(0) = 0.

Using this, it is easy to get the answer "by hand" as

2*S(3) + 1 + 2 + 2*S(1) + 2 + 2 + 4 + 6 + 8 = 194785

Note: 1+2+...+9 = 45

Yes, I will help. Just try to write something in Maple, however crude, for the Euler method for a single equation. Then post it here, send me an email, and I'll help.

Oh, by the way, these methods are pre-coded into Maple's dsolve command, but I guess that you have been assigned to write them from scratch. Well, at least that gives you something to compare your answers with. See ?dsolve,numeric,classical .

@abbeykabir So the simple Newton iteration and fsolve return the same answers for your equations.

@abbeykabir So the simple Newton iteration and fsolve return the same answers for your equations.

I've never been a Mathematica user, nor have I made a comparison, so I may not be who you want to hear from. From the little bits of Mathematica that I've seen, it has a hideous bracketing syntax, using square brackets instead of parentheses and curly braces instead of square brackets.

I also object to the underlying code being hidden.

@abbeykabir Okay, good. (You need to reverse the direction of the inequality.) Yes, it's called convergence. In the multivariate case X[i+1] - X[i] is a vector. What is the analog of absolute value for vectors?

@abbeykabir Okay, good. (You need to reverse the direction of the inequality.) Yes, it's called convergence. In the multivariate case X[i+1] - X[i] is a vector. What is the analog of absolute value for vectors?

@yangtheary The title of your reply indicates that you are looking for a polynomial answer. My answer is based on seeing a pattern, and is not a polynomial.

A polynomial answer can always be obtained by a trivial formula, so is rather boring. The polynomials produced are usually not obvious or interesting, and their extrapolations usually do not follow the "obvious" and "logical" pattern of the sequence.

CurveFitting:-PolynomialInterpolation([[1,1], [2,3], [3,6], [4,12], [5,24]], n);

Say, what is the theme or purpose of your current series of questions?