Dear Users!

Hope everyone is fine here. I want to formulate the table like give bellow (Table 5.17) in maple so that I can copy it in word file and can edit.

The values of y[1,1],y[2,1],y[2,2],y[3,1],y[3,2],y[3,3]...y[nops(HAq),nops(HAq)] present in the following maple code. Thanks in advance

Refine_Extrapolation.mw

Hi,

I want to solve this system of PDEs. Please let me know how I can solve it.

Kindly find both my code written in Maple and the image of the problem.

Best,

PDE.mw

Is there a way to make a library file that automatically has the functions/procedures loaded on startup and after it any new or open ".mw" can use functions/procedures from library with no redefinition?

It's ok isolate command? I need the solution sin(a)=+-1/(3^0.5)

Let A a (linear) partial differential operator and f=f(x, y, t) a function of space (x, y) and time (t).
Let D_XY=[a, b] x [c, d], D_T=[0..e] and  d_XY the boundary of D_XY.
Is it possible, with Maple 2015, to solve numerically the pde Af=0 in the open domain  D_XY * D_T
with Dirichlet conditions on d_XY and initial condition f(D_XY, 0)?
It seems that the option 'numeric' of pdsolve doesn't work with more than 1 "non time" independent variable:
Error, (in pdsolve/numeric/process_PDEs) can only numerically solve PDE with two independent variables, got {t, x, y}

Nevertheles I seem to remember seeing this on Mapleprime (?)
If Maple 2015 can't do it, can Maple 2020?

Thanks in advance

• Remark: Af=0 is the heat equation with rho=Cp=lambda=1.
  I guess I could code the alternate directions method to transform  Af=0 into a sequence A_xf=0,  A_yf=0,  A_xf=0 ... of 1D diffusion equations but I'm a little bit lazzy and I'm waiting for your feedback before doing this.

Dear Users!

Hope everyone fine here. I want to collocate Vector IntXYZ1 and IntXYZ2 present in file Q1 in such a way that the first M1M2 + 2(M3-1)M2 + 2(M3-1)(M1-2) rows are zero and other rows are collocated at x=(i-1)/(M1-1), y=(j-1)/(M2-1), t=(k-1)/(M3-1) for i = 2,3,…,M1-1, j = 2,3,…,M2-1, k = 2,3,…,M3 as given as XX (of order 27 by 27 with first 25 rows are zero) for M1=M2=M3=3

I am waiting for positive response to fix this issue. Thanks in advance

Q1.mw

Hi, 

Why does the use of  global  at the top level of a worksheet is no longer accepted in the most recent versions of Maple (it still was in Maple 2015), but only within procedures?

TIA

Hi 

How to add a legend to Statistics:-Histogram?

This could be particularly useful to compare histograms, for instance in

S := Statistics:-Sample(Normal(0, 1), 1000):
T := Statistics:-Sample(Normal(1, 1), 1000):

plots:-display(
  Statistics:-Histogram(S, color=gold, transparency=0.3, legend="N(0,1)"),
  Statistics:-Histogram(T, transparency=0.3, legend="N(1,1)")
);

But doing this generates the error Error, (in Statistics:-Histogram) display does not accept the legend option

And yes indeed, even this command

h := Statistics:-Histogram(S, legend="N(0,1)")

already produces the same error.

After having examined the structure of h and using a way Carl Love gave here How to change the colour inn Statistics:-Sunflower?  I finally obtained the expected plot.
 

HS := Statistics:-Histogram(S, color=gold, transparency=0.3):
HT := Statistics:-Histogram(T, transparency=0.3):

hs := evalindets([op(HS)], specfunc(COLOUR), c-> (c, LEGEND("N(0,1)")) ):
ht := evalindets([op(HT)], specfunc(COLOUR), c-> (c, LEGEND("N(1,1)")) ):

PLOT(op(hs), op(ht))

But this rather long a way to proceed (Note: it seems that the overrideoption  that acer suggested in this prevous thread doesn't "work" here?)
Do you have any idea if there is a simpler solution?

TIA

Dear Users!
Hope everyone fine here. I have a vector V and want a new vector after transformation like

V := Vector(5, {(1) = 2, (2) = 3, (3) = -1, (4) = 9, (5) = 7});

after square transformation of V I got a new vector W like bellow

W := Vector(5, {(1) = 4, (2) = 9, (3) = 1, (4) = 81, (5) = 49});

and similarly sin transformation of V give the following matrix as

U := Vector(5, {(1) = sin(2), (2) = sin(3), (3) = sin(-1), (4) = sin(9), (5) = sin(7)});
Please help me to get vectors W and U.

Dear Users!
Hope everyone fine here. I tried (as given bellow) to find the solution of nonlinear system of PDEs via FDM. To solve system of nonlinear equations I used newton raphson method and for higher value of like Mx > 8 the matrix G and G1 (mentioned as red) take alot of time. Can anyone help me to reduce the computational time? Becuase I have to evealuate the solution for Mx = 50.

restart; Digits := 30; with(LinearAlgebra);
T := 1; L := 3; N := 30; Mx := 5; `Δx` := L/(1.*Mx); `Δt` := T/(1.*N);
for i from 0 while i <= Mx do
u[i, 0] := 0.; u[i, -1] := u[i, 1]; tau[i, 0] := 0.; theta[i, 0] := 0.; theta[i, -1] := theta[i, 1]
end do;
for n from 0 while n <= N do u[0, n] := 0.; u[Mx, n] := 0.; theta[0, n] := 1.; theta[Mx, n] := 0.
end do;
for n from 0 while n <= N-1 do
print("Simulation in proccess at time-level n", n+1);
for i while i <= Mx-1 do
Ru[i, n] := simplify((u[i+1, n+1]-u[i+1, n])/`&Delta;t`+(u[i+1, n+1]-2*u[i+1, n]+u[i+1, n-1])/`&Delta;t`^2-(u[i+1, n+1]-2*u[i, n+1]+u[i-1, n+1])/`&Delta;x`^2+25.*(u[i+1, n+1]+(u[i+1, n+1]-u[i+1, n])/`&Delta;t`)-1.5*(theta[i, n]+(theta[i, n+1]-theta[i, n])/`&Delta;t`));
`R&theta;`[i, n] := simplify((theta[i+1, n+1]-theta[i+1, n])/`&Delta;t`+(theta[i+1, n+1]-2*theta[i+1, n]+theta[i+1, n-1])/`&Delta;t`^2-(theta[i+1, n+1]-2*theta[i, n+1]+theta[i-1, n+1])/((15.)*`&Delta;x`^2)-((u[i, n+1]-u[i-1, n+1])/`&Delta;x`)^2/(3.)) end do;
for i while i <= Mx-1 do
`R&tau;`[i, n] := simplify(tau[i+1, n+1]+(tau[i+1, n+1]-tau[i+1, n])/`&Delta;t`-1.5^(-1/4)*(u[i+1, n+1]-u[i, n+1])/`&Delta;x`)
end do;
Sys := `<,>`(seq(Ru[i, n], i = 1 .. Mx-1), seq(`R&tau;`[i, n], i = 1 .. Mx-1), seq(`R&theta;`[i, n], i = 1 .. Mx-1));
V := `<,>`(seq(u[i, n+1], i = 1 .. Mx-1), seq(theta[i, n+1], i = 1 .. Mx-1), seq(tau[i, n+1], i = 2 .. Mx));
G := Matrix(3*(Mx-1), proc (i, j) options operator, arrow; diff(Sys[i], V[j]) end proc); G1 := MatrixInverse(G);
X[n, 0] := Vector(1 .. 3*(Mx-1), 1);
for k1 from 0 to r do
X[n, k1+1] := eval(V-G1 . Sys, Equate(V, X[n, k1]))
end do;
Sol[n] := Equate(V, X[n, r+1]); assign(op(Sol[n]));
if n > 0 then
U := eval(`<,>`(seq(u[i1, n+1], i1 = 1 .. Mx)-seq(u[i1, n], i1 = 1 .. Mx))); Noru[n+1] := Norm(%, 2); print("L[&infin;] norm of &tau;(x,y,t) at time level = ", %);
Theta := eval(`<,>`(seq(theta[i1, n+1], i1 = 0 .. Mx)-seq(theta[i1, n], i1 = 0 .. Mx))); `Nor&theta;`[n+1] := Norm(%, 2); print("L[&infin;] norm of &theta;(x,y,t) at time level = ", %) else print("n < 0")
end if end do

Special request to:
@acer @Carl Love @Kitonum @Preben Alsholm

Dear Users!

I want to find the solution of the solution of PDEs as given bellow:

restart;
PDE1 := diff(u(y, t), t)+diff(u(y, t), t, t) = diff(u(y, t), y, y)-u(y, t);
PDE2 := v(y, t)+diff(tau(y, t), t) = diff(u(y, t), y);
ICandBC := {tau(y, 0) = 0, u(0, t) = 0, u(3, t) = 0, u(y, 0) = 0, (D[2](u))(y, 0) = 0};
pds := pdsolve({PDE1, PDE2}, ICandBC, numeric);

But got the following error

Error, (in pdsolve/numeric/process_PDEs) number of dependent variables and number of PDE must be the same
Kindly help me to fix this error. I shall be very thankful. 

Special request to:
@acer @Carl Love @Kitonum @Preben Alsholm

Hi, 

I have always asked myself this question: why do the colon after the proc(...) statement generate an error if the following statement is local or global?
(the third example is here to show that no error occurs if local is omitted... the warning is of course obvious)

restart:
interface(version);
Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895

f := proc(x) local y: y:=x+1 end proc:

g := proc(x): local y: y:=x+1 end proc:
Error, unexpected `local` declaration in procedure body

h := proc(x): y:=x+1 end proc:
Warning, `y` is implicitly declared local to procedure `h`

TIA

I just got a "new" graphics card, NVIDIA GT630, and was wondering whether the CUDA capabilities are accessible. But no luck:

CUDA:-Enable();

Error, (in CUDA:-Enable) CUDA not supported on the current system (see CUDA,supported_hardware for more information)

The CUDA help page with the example, when run, just shows a host of error messages.

I have OS X 10.11.6, the above mentioned GT630 card with claimed 384 CUDA cores and 2 GB of VRAM; NVIDIA WebDriver 346.03.15f16 for the card (i.e. latest for this OS) and NVIDIA CUDA driver 8.0.90 (again, latest for this OS as far as I can tell). My Maple is 2015.2. All this running on a MacPro 4,1.

I am not having great illusions about the performance I should get (this is not a state-of-the-art card today), but it seems to me this combination should be working with Maple 2015 and not throw an error, shouldn't it? Checking the system extensions: CUDA.kext is loaded and its dependencies are satisfied, so I don't see any problem there.

Am I missing something?

M.D.

Hi, 
The result below surprises me.
Why does  rgf_findrecur return a result instead of saying that there is no homogeneous linear recurrence of order 1?

interface(version)

Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895


genfunc:-rgf_findrecur(1, [1, 2, 3, 4], t, n);
                       t(n) = 2 t(n - 1)

PS: maybe this was a problem in Maple 2015, if it has been corrected since just let me know

Why do I get this wrong result when I try to solve formally this ode (note that acer has already obtained its implicit form here implicit)

restart:
interface(version)
Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895

edo := diff(y(x), x, x) = 1/y(x) - x*diff(y(x), x)/y(x)^2;
ic  := y(0)=1, D(y)(0)=0:

dsolve({edo, ic}, y(x));
eval(edo, %)
                                        / d      \
                                      x |--- y(x)|
               d  / d      \    1       \ dx     /
              --- |--- y(x)| = ---- - ------------
               dx \ dx     /   y(x)          2    
                                         y(x)     
                    
                            y(x) = 1

                             0 = 1

Thanks in advance