Download fourthLINEARBOUD042021.mw
 

Download fourthLINEARBOUD042021.mw
 

Download fourthLINEARBOUD042021.mw
 

Download fourthLINEARBOUD042021.mw

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;
 

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

Download ITRATIVE.mw

 PLS

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

ATTACHED IS THE MAPLECODE  STARTED WITH.

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

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.?

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

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

How to come to the result 2764,6 radians?

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?

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

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

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.

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?

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?

As part of the class I am teaching in biofluid mechanics, the students are learning about the Buckingham Pi theory for finding dimensionless groups (pi-groups).  The process involves the dimensions of parameters in terms of their basic units of measure: mass, M, length, L, and time, T.  Fore example, fluid density is M/L³ .  A typical step is to represent a product of parameters in terms of these measures raised to exponents.  Here is an example

(M/LT)^a(M/L³)^b(L²)^c

where the exponents a,b,c are to be determined. What command(s) will massage this form to look like

M^a+b  L^2c-3b-a T^-a  ?

Cheers