## Boundary Value Problem, some iteration without eva...

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PLS FIND ATTACHED A MAPLE CODE TO SOLVE SOME BOUNDARY VALUE PROBLEM, BUT IT JUMP SOME ITERATION WITHOUT EVALUATION WHICH END UP WITH INACCURATE SOLUTION.

> restart;
> with(LinearAlgebra);
> exp(1) := 2.7182818284590452354;
> alpha := .975;
> NULL;
> st := time[real]();
> for i to 4 do for j from 0 by .1 to 4-exp(1) do Exact[j] := evalf(ln(exp(1)+j)); Y[0] := proc (x) options operator, arrow; 1+x/exp(1)+(1/4)*((exp(1))^2-8*exp(1)+24*ln(2)*exp(1)-32)*x^2/(exp(1)*(16-8*exp(1)+(exp(1))^2))+(1/4)*(16*ln(2)*exp(1)-16-8*exp(1)+(exp(1))^2)*x^3/((-64+48*exp(1)-12*(exp(1))^2+(exp(1))^3)*exp(1)) end proc; Ics := Z(0) = 1, (D(Z))(0) = 1/exp(1), Z(4-exp(1)) = evalf(ln(4)), (D(Z))(4-exp(1)) = 1/4; f := proc (x) options operator, arrow; 0 end proc; p := proc (x) options operator, arrow; 0 end proc; q := proc (x) options operator, arrow; 0 end proc; r := proc (x) options operator, arrow; 0 end proc; u := proc (x) options operator, arrow; 0 end proc; eq[i] := diff(Z(x), `\$`(x, 4)) = (1-alpha)*(diff(Y[i-1](x), `\$`(x, 4)))+alpha*(-6*convert(taylor(exp(-4*Y[i-1](x)), x = 0, 20), polynom)); s[i] := dsolve({Ics, eq[i]}, Z(x)); Y[i] := unapply(op(2, s[i]), x); App[j] := evalf(Y[i](j)); Er[j] := abs(App[j]-Exact[j]); print([App[j], Exact[j], Er[j]]) end do end do; time[real]()-st;

## Invalid Subscript selector - Maple 14...

Hello

The following maple command returns an error in Maple 14 (internal error in Typesetting ... "invalid subscript selector") but not in Maple 2017.

f:=(l::list)-> eval([y,y*z-x,-15*x*y-x*z-x],[x,y,z]=~l):

What did I miss?

Many thanks

Ed

## Iteration formula...

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 Error, invalid operator parameter name > restart; > with(LinearAlgebra); > for k from 0 to 1 do;    u(t,x):=1+x;  u[k+1](t,x):=1+x-(∫)[0]^(t)(diff(u[k],x) +2+s+x)ⅆs;  U[k+1](t,x)=u[k+1 ](t,x)-(u[k](t,0)-(1+t));  end      ;
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PLS

HOW CAN I ITERATE THIS PDE IN THE FORM OF PICARD ITERTION.

ATTACHED IS THE MAPLECODE  STARTED WITH.

## Issues with eps exported files...

Hello,

Here is the code I used to generate the image:

`densityplot(x,x=0..1,y=-0..0.1,colorstyle=HUE,style=patchnogrid,scaling=constrained,view=[0..1,0..0.1],axes=none);`

Then, I exported the image in a eps format. When the file is displayed, white lines appear as a grid. The problem comes from Maple and not from the softwares used to visualize the image. I tried so many things to solve that but...

How to solve the problem?

Thank you.

Jaqr

## Use of ATLAS in calculation of Riemannian metric i...

I wish to calculate connection, curvature, Ricci curvature etc. for a

Riemannian metric given as follows: there is an orthogonal frame of vector

fields with stipulated Lie bracket relations between them. The frame is

orthogonal but not orthonormal, and the lengths of its vector fields are functions

of a single function on the manifold. Given these metric values on the frame and the

Lie bracket relations, the covariant derivatives are in principle computable from the

Koszul formula, hence connection and curvature are all determined.

When I try to define the metric using a dual coframe in ATLAS's Metric

routine, it allows me to define it but claims there is not actual curvature.

From the help it seems the coframes used in this routine are always given

as differentials of coordinates. Is there a way to get the metric via the data

given above without putting in by hand all the different Koszul formulas etc.?

## How to display last few digits?...

If I input 3^665 the whole number is displayed. How to display only last few digits?

## How to obtain the result in radians...

When I make the input 2*pi*440 the output is pi880.

How to come to the result 2764,6 radians?

## How to turn into complex exponential Fourier serie...

cos(440*2*pi*t)+cos(554*2*pi*t)+cos(659*2*pi*t)

How to turn the above row into complex exponential Fourier series?

## What is the input for mixed fractions?...

For example how to input the mixed fraction 3 1/7? What are keys for super- and subscript?

## random digits or a sequence?...

How to make Maple determine whether the following is a sequence with a rule behind it or just random fractions:

3^893/2^1415, 3^1040/2^1648, 3^2192/2^3474, 3^3776/2^5984, 3^3910/2^6197, 3^5514/2^8739

## How to convert to trigonometric form...

How should I proceed to convert 2ln(3) -3ln(2)  to trigonometric form in Maple?

## Is such a sequence possible?...

Is it possible to construct in Maple the following sequence of ascending fifths?:

3/2, 3^2/2^3, 3^3/2^4, 3^4/2^6, 3^5/2^7, 3^6/2^9, 3^7/2^11, 3^8/2^12 and so on. The result always more than 1 and less than 2.

## How to find a pattern in a sequence in Maple...

Given a sequence for example: 8, 32,128,512,2048 and so on. Suppose we do not know it is 2^(2n +1). How to make Maple to find the principle?

## What input should I write 3^665/2^x=y...

In the fraction 3^665/2^x=y, where y is more than 1 and less than 2, I want to know the value of x. What input should I write, please?