@emma hassan Your f contains a constant term c[1,0]. This term disappears when you take the derivative. Thus, it does not appear in any of the equations E[r]. Thus, fsolve does not provide any value for it. So, when you try to use u, it still has an unevaluated c[1,0] in it.

@emma hassan Your f contains a constant term c[1,0]. This term disappears when you take the derivative. Thus, it does not appear in any of the equations E[r]. Thus, fsolve does not provide any value for it. So, when you try to use u, it still has an unevaluated c[1,0] in it.

It seems that interpolant only applies to BVPs, whereas the quote about an option "interpolation" is on a help page for rkf45, an IVP method. There also seems to be an undocumented (as far as I can tell) and inactive (as far as I can tell) option interpolate. Here's my attempts to use the options.

restart:
dsolve({diff(y(x),x)=y(x), y(0)=1}, {y(x)}, numeric, method= rkf45, interpolant= false);
Error, (in dsolve/numeric/an_args/SC) keyword was 'interpolant', optional keyword must be one of 'abserr', 'differential', 'event_doublecross', 'event_initial', 'event_iterate', 'event_maxiter', 'event_pre', 'event_project', 'event_relrange', 'event_stepreduction', 'events', 'implicit', 'initstep', 'interpolate', 'interr', 'maxfun', 'maxstep', 'minstep', 'optimize', 'output', 'projection', 'range', 'relerr', 'startinit', 'steppast'

dsolve({diff(y(x),x)=y(x), y(0)=1}, {y(x)}, numeric, method= rkf45, interpolate= false);
Warning, the 'interpolate' option has been removed, ignored...
proc(x_rkf45)  ...  end;

Could you say precisely on which help page you saw this advice? Look at the title bar of help window. It should say something like "Maple 16 Help - [dsolve,numeric_bvp,advanced]".

Could you be more precise about what you mean by "huge matrix DE"?

That does obscure the gridlines.

That does obscure the gridlines.

@ThU I guess that by "converted to radicals" you mean radicals without I. If so, then no, it cannot be thus converted. There are subexpressions essentially of the form

convert(sin(arctan(x)/3), exp);

The 1/3 coefficient of the arctan makes all the difference.

@ThU I guess that by "converted to radicals" you mean radicals without I. If so, then no, it cannot be thus converted. There are subexpressions essentially of the form

convert(sin(arctan(x)/3), exp);

The 1/3 coefficient of the arctan makes all the difference.

In order for "greatest common divisor" to be well defined, you need to have a concept of divisor and an ordering of the divisors so that you can determine which is greatest (the degree is used to order polynomials).

So, can you show some examples of what you would mean by divisor and explain what you would use instead of the degree?

@lettie079 

Like this:

L:= [1,2,3,1,2,3]:
[L[1..-4][], {L[-3..-1][]}];
                      [1, 2, 3, {1, 2, 3}]

@lettie079 Yes, you could use an Array instead. An Array would be especially appropriate in a situation where you want the final list to be in a certain order and you know a close upper bound on the final number of elements.

@lettie079 Yes, you could use an Array instead. An Array would be especially appropriate in a situation where you want the final list to be in a certain order and you know a close upper bound on the final number of elements.

@Christopher2222 Without the assume, it complains that it cannot determine whether X and Y are distinct points.

@Christopher2222 Without the assume, it complains that it cannot determine whether X and Y are distinct points.

@J4James Looking at any standard Numerical Analysis textbook, you will find numerous proofs of the accuracy of numerical schemes. These proofs put upper bounds on the errors. But you originally asked about residuals, not upper bounds. The residuals cannot be known unless the exact solution is known.