MaplePrimes Questions

I solve a boundary value problem for a linear system of first order PDEs
in the unknowns u(x, t) and "v(x,t)."  Ultimately, I am interested in the graph
of the function v(0, t) but numerical artifacts distort that graph badly by
imposing spurious oscillation.

Is there a way to maneuver the calculations to obtain the graph of v(0, t)
without the oscillation?

restart;

pde1 := diff(u(x,t),t)=diff(v(x,t),x);

diff(u(x, t), t) = diff(v(x, t), x)

pde2 := diff(u(x,t),x)=v(x,t);

diff(u(x, t), x) = v(x, t)

ibc := u(x,0)=1, u(0,t)=0, u(1,t)=0;

u(x, 0) = 1, u(0, t) = 0, u(1, t) = 0

dsol := pdsolve({pde1,pde2}, {ibc}, numeric, spacestep=0.01, timestep=0.01);

_m139872446597344

dsol:-value(output=listprocedure):
my_u := eval(u(x,t), %):
my_v := eval(v(x,t), %%):

plot3d(my_u(x,t), x=0..1, t=0..0.5);

plot3d(my_v(x,t), x=0..1, t=0..0.5);

The oscillations are numerical artifacts.  Can they be avoided?

plot(my_v(0,t), t=0..0.5);

A side comment: By eliminating vbetween the two PDEs we see that u
satisfies the standard heat equation, thus vis the flux.  The expression
v(0, t) expresses the heat flux at the boundary, and that's what I am after.
 


 

Download calculating-flux-in-the-heat-equation.mw

I open a completely new document, type in a few simple expressions and get this weird complex number out. Can someone pleas help me fix this?

In this question at here https://tex.stackexchange.com/questions/503745/how-can-i-get-correct-the-point-a-and-b-automatically-in-this-picture/503838?noredirect=1#comment1272706_503838
The points A and B lie on the circle is intersection of the sphere x^2 + y^2 + (z-3)^2 = 25 and the plane z = 0. 
How can I find coordinates of the points A and B by Maple?

 

searchtext and SearchText do not work well with non-ASCII characters.
Strangely, StringTools:-Search is OK.

restart;
m:=convert([77,97,116,104,195,169,109,97,116,105,113,117,101], bytes);
                      m := "Mathématique"
seq(searchtext(m[i..7], m), i=1..7);
                      1, 0, 0, 4, 0, 0, 1
seq(SearchText(m[i..7], m), i=1..7);
                      1, 0, 0, 4, 0, 0, 7
seq(StringTools:-Search(m[i..7], m), i=1..7);
                      1, 2, 3, 4, 5, 6, 7

 

I'm a Maple novice.  I have two questions.  (1) I'm trying to use Maple to confirm some Fourier transforms of selected probability density functions.  In general I've succeeded, but Maple fails to find the Fourier transform of the pdf of a logistic random variable with mean 0.  Please explain how I can get Maple to carry out this request.  I've attached a Maple file with my work to this question.  (2) At several points in my computations, I wish to substitute 2*Pi*xi for omega.  I have an expression containing two omegas.  If I use algsubs(), only one of the two omegas is replaced.  I have to use subs() to replace both omegas.  Why is this?
 

Use Maple to confirm selected Fourier transform of logistic random variable

with(inttrans)

[addtable, fourier, fouriercos, fouriersin, hankel, hilbert, invfourier, invhilbert, invlaplace, invmellin, laplace, mellin, savetable]

(1)

assume(a > 0)

NULL

"f(x):=((e)^(x/(a)))/(a*(1+(e)^(x/(a)))^(2))"

proc (x) options operator, arrow, function_assign; exp(x/a)/(a*(1+exp(x/a))^2) end proc

(2)

int(f(x), x = -infinity .. infinity)

1

(3)

fourier(f(x), x, omega)

fourier(exp(x/a)/(1+exp(x/a))^2, x, omega)/a

(4)

"f(x) := 1/(4*a*(cosh(x/(2*a)))^(2))"

proc (x) options operator, arrow, function_assign; (1/4)/(a*cosh((1/2)*x/a)^2) end proc

(5)

int(f(x), x = -infinity .. infinity)

1

(6)

fourier(f(x), x, omega)

fourier(1/(exp((1/2)*x/a)+exp(-(1/2)*x/a))^2, x, omega)/a

(7)

Wikipedia's article on "Logistic distribution" gives a characteristic function that implies that the Fourier transform of this pdf should equal Pi*a*omega/sinh(Pi*a*omega).

Unit rectangular function

rect := proc (x) options operator, arrow; Heaviside(x+1/2)-Heaviside(x-1/2) end proc

proc (x) options operator, arrow; Heaviside(x+1/2)-Heaviside(x-1/2) end proc

(8)

fourier(rect(a*x), x, omega)

2*sin((1/2)*omega/a)/omega

(9)

algsubs(omega = 2*Pi*xi, 2*sin((1/2)*omega/a)/omega)

2*sin(Pi*xi/a)/omega

(10)

subs(omega = 2*Pi*xi, 2*sin(Pi*xi/a)/omega)

sin(Pi*xi/a)/(Pi*xi)

(11)

``

NULL


 

Download Logistic_pdf.mw

 

restart;


K := -3;
                               -3
m := 1;
                               1
w := -4*K;
                               12
alpha[0] := -2;
                               -2
alpha[1] := 0;
                               0
a := 2;
                               2
b := 3;
                               3
                               1
beta[1] := (12*(m^2+K))/(a+b);
                              -24
                              ---
                               5 
xi := -t*w+x+y;
                         -12 t + x + y

F := -sqrt(-K)*tanh(sqrt(-K)*xi);
                (1/2)     / (1/2)                \
              -3      tanh\3      (-12 t + x + y)/
U := alpha[0]+alpha[1]*(m+F)+beta[1]/(m+F);
                                 24                     
        -2 - -------------------------------------------
               /     (1/2)     / (1/2)                \\
             5 \1 - 3      tanh\3      (-12 t + x + y)//
                               1
y := 0;
                               0

plot3d(U, x = -10 .. -10, t = -10 .. 10);

t := 0;
                               0
plot(U, x = -10 .. 10);

How can find order of convergence  for multiple roots for example x-2*f(x)/Df(x)

WHICH have quadratic  order of convergence how find out in maple software????

 

How do I calculate the intersection curve between a plane and a drop?
The "drop" is defined in the following way:

R1 := 3.;R2 := 1.0;DR := 4;g := R2 + DR;

f1 := h -> sqrt(R1^2 - h^2);
f2 := h -> sqrt(g^2 - h^2);
f3 := h -> (1 - h/g)*f1(h*R1/g) + h*f2(h)/g;
f4 := h -> sqrt(1/2*g - 1/2*h);
f5 := h -> (1 - h/g)*f3(h) + h*f4(h)/g;
gg := h -> piecewise(h < 0, f1(h), 0 <= h, f5(h));#Radius depending on the z-position h
cir := (h, phi, R) -> <sin(phi)*R, cos(phi)*R, h>; # a circle at the hight h with radius R
#The plane is placed inside the drop.
n := (x, y, z) -> <x, y, z>/sqrt(x^2 + y^2 + z^2);

# the following lines show, how it looks like:
with(plots);
with(plottools);
dro1 := plot3d(cir(h, phi, gg(h)), h = -R1 .. g, phi = 0 .. 2*Pi, scaling = constrained, orientation = [-60, 72, 0]);
plotDropWithPlane := (x, y, z) -> display(dro1, arrow(Vector([0, 0, 0]), 2*R1*n(x, y, z), 0.2, 0.4, 0.1, cylindrical_arrow, fringe = blue, color = "Green"), implicitplot3d(x*x1 + y*y1 + z*z1 = 0, x1 = -R1 .. R1, y1 = -R1 .. R1, z1 = -R1 .. g, color = blue));
plotDropWithPlane(3, 1, 2);

#I'm searching a function like
fintersect:=theta-><"?,?,?>"

Any idea how to solve?

Best regards,

Andreas

unprotect(D); f := proc (x, y) options operator, arrow; (295849/5841396)*x^2-(29441/324522)*y*x+(33995/216348)*y^2-(5989/14751)*x+(3635/4917)*y+1 end proc; 295849 2 29441 33995 2 5989 f := (x, y) -> ------- x - ------ y x + ------ y - ----- x 5841396 324522 216348 14751 3635 + ---- y + 1 4917 coeffs(f(x, y)); -5989 3635 295849 33995 -29441 1, -----, ----, -------, ------, ------ 14751 4917 5841396 216348 324522 A, B, C, D, E, F := %; -5989 295849 33995 -29441 3635 A, B, C, D, E, F := 1, -----, -------, ------, ------, ---- 14751 5841396 216348 324522 4917

Is there any way we can get maple to tell us which variable we are recursively assigning? 

I would like to simplify

sin(4*pi*w)/sin(2*pi*w) 

The answer I am looking for is 2*cos(2*pi*w).

Does anyone have an idea how to do this is Maple? Some earlier version of Maple I used could do this, 

simplify( sin(4*pi*w)/sin(2*pi*w) ) =  2*cos(2*pi*w)

There a plenty of different trigonometric representations for the answer, so my hypothesis is that I should somehow tell to Maple which I am looking for. 

For example

Gives

Which is better, but still not the answer I am looking for

Best Regards,

P

 

 

 

RootOf(_Z^2*beta*h[1]-alpha*l[1]*l[2], label = _L2)


 

with(VectorCalculus)

pde := Laplacian(u(r, t), 'cylindrical'[r, theta, z]) = diff(u(r, t), t)

iv := {u(1, t) = 0, u(4, t) = 0, u(r, 0) = r}

dsol := pdsolve(pde, iv, numeric):-value(output = listprocedure)

sd := rhs(dsol[3])

proc () local tv, xv, solnproc, stype, ndsol, vals; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; Digits := trunc(evalhf(Digits)); solnproc := proc (tv, xv) local INFO, errest, nd, dvars, dary, daryt, daryx, vals, msg, i, j; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; table( [( "soln_procedures" ) = array( 1 .. 1, [( 1 ) = (18446746697122892894)  ] ) ] ) INFO := table( [( "extrabcs" ) = [0], ( "totalwidth" ) = 6, ( "spacevar" ) = r, ( "dependson" ) = [{1}], ( "solmatrix" ) = Matrix(21, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0}, datatype = float[8], order = C_order), ( "matrixproc" ) = proc (v, vp, vpp, t, x, k, h, n, mat) local _s1, _s2, xi; _s1 := 4*h^2; _s2 := -(h^2+k)/(h^2*k); mat[3] := 1; mat[6*n-3] := 1; for xi from 2 to n-1 do mat[6*xi-3] := _s2; mat[6*xi-4] := -(h-2*x[xi])/(_s1*x[xi]); mat[6*xi-2] := (h+2*x[xi])/(_s1*x[xi]) end do end proc, ( "leftwidth" ) = 1, ( "solmat_i1" ) = 0, ( "eqnords" ) = [[2, 1]], ( "allocspace" ) = 21, ( "method" ) = theta, ( "theta" ) = 1/2, ( "solmat_i2" ) = 0, ( "intspace" ) = Matrix(21, 1, {(1, 1) = .0, (2, 1) = .0, (3, 1) = .0, (4, 1) = .0, (5, 1) = .0, (6, 1) = .0, (7, 1) = .0, (8, 1) = .0, (9, 1) = .0, (10, 1) = .0, (11, 1) = .0, (12, 1) = .0, (13, 1) = .0, (14, 1) = .0, (15, 1) = .0, (16, 1) = .0, (17, 1) = .0, (18, 1) = .0, (19, 1) = .0, (20, 1) = .0, (21, 1) = .0}, datatype = float[8], order = C_order), ( "depords" ) = [[2, 1]], ( "rightwidth" ) = 0, ( "depeqn" ) = [1], ( "stages" ) = 1, ( "spacepts" ) = 21, ( "indepvars" ) = [r, t], ( "minspcpoints" ) = 4, ( "startup_only" ) = false, ( "eqndep" ) = [1], ( "depdords" ) = [[[2, 1]]], ( "adjusted" ) = false, ( "norigdepvars" ) = 1, ( "solvec4" ) = 0, ( "explicit" ) = false, ( "solution" ) = Array(1..3, 1..21, 1..1, {(1, 1, 1) = .0, (1, 2, 1) = .0, (1, 3, 1) = .0, (1, 4, 1) = .0, (1, 5, 1) = .0, (1, 6, 1) = .0, (1, 7, 1) = .0, (1, 8, 1) = .0, (1, 9, 1) = .0, (1, 10, 1) = .0, (1, 11, 1) = .0, (1, 12, 1) = .0, (1, 13, 1) = .0, (1, 14, 1) = .0, (1, 15, 1) = .0, (1, 16, 1) = .0, (1, 17, 1) = .0, (1, 18, 1) = .0, (1, 19, 1) = .0, (1, 20, 1) = .0, (1, 21, 1) = .0, (2, 1, 1) = .0, (2, 2, 1) = .0, (2, 3, 1) = .0, (2, 4, 1) = .0, (2, 5, 1) = .0, (2, 6, 1) = .0, (2, 7, 1) = .0, (2, 8, 1) = .0, (2, 9, 1) = .0, (2, 10, 1) = .0, (2, 11, 1) = .0, (2, 12, 1) = .0, (2, 13, 1) = .0, (2, 14, 1) = .0, (2, 15, 1) = .0, (2, 16, 1) = .0, (2, 17, 1) = .0, (2, 18, 1) = .0, (2, 19, 1) = .0, (2, 20, 1) = .0, (2, 21, 1) = .0, (3, 1, 1) = .0, (3, 2, 1) = .0, (3, 3, 1) = .0, (3, 4, 1) = .0, (3, 5, 1) = .0, (3, 6, 1) = .0, (3, 7, 1) = .0, (3, 8, 1) = .0, (3, 9, 1) = .0, (3, 10, 1) = .0, (3, 11, 1) = .0, (3, 12, 1) = .0, (3, 13, 1) = .0, (3, 14, 1) = .0, (3, 15, 1) = .0, (3, 16, 1) = .0, (3, 17, 1) = .0, (3, 18, 1) = .0, (3, 19, 1) = .0, (3, 20, 1) = .0, (3, 21, 1) = .0}, datatype = float[8], order = C_order), ( "pts", r ) = [1, 4], ( "spaceidx" ) = 1, ( "solmat_v" ) = Vector(126, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0, (43) = .0, (44) = .0, (45) = .0, (46) = .0, (47) = .0, (48) = .0, (49) = .0, (50) = .0, (51) = .0, (52) = .0, (53) = .0, (54) = .0, (55) = .0, (56) = .0, (57) = .0, (58) = .0, (59) = .0, (60) = .0, (61) = .0, (62) = .0, (63) = .0, (64) = .0, (65) = .0, (66) = .0, (67) = .0, (68) = .0, (69) = .0, (70) = .0, (71) = .0, (72) = .0, (73) = .0, (74) = .0, (75) = .0, (76) = .0, (77) = .0, (78) = .0, (79) = .0, (80) = .0, (81) = .0, (82) = .0, (83) = .0, (84) = .0, (85) = .0, (86) = .0, (87) = .0, (88) = .0, (89) = .0, (90) = .0, (91) = .0, (92) = .0, (93) = .0, (94) = .0, (95) = .0, (96) = .0, (97) = .0, (98) = .0, (99) = .0, (100) = .0, (101) = .0, (102) = .0, (103) = .0, (104) = .0, (105) = .0, (106) = .0, (107) = .0, (108) = .0, (109) = .0, (110) = .0, (111) = .0, (112) = .0, (113) = .0, (114) = .0, (115) = .0, (116) = .0, (117) = .0, (118) = .0, (119) = .0, (120) = .0, (121) = .0, (122) = .0, (123) = .0, (124) = .0, (125) = .0, (126) = .0}, datatype = float[8], order = C_order, attributes = [source_rtable = (Matrix(21, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0}, datatype = float[8], order = C_order))]), ( "maxords" ) = [2, 1], ( "solvec5" ) = 0, ( "fdepvars" ) = [u(r, t)], ( "spacestep" ) = .150000000000000, ( "banded" ) = true, ( "PDEs" ) = [(diff(u(r, t), r)+r*(diff(diff(u(r, t), r), r)))/r-(diff(u(r, t), t))], ( "erroraccum" ) = true, ( "autonomous" ) = true, ( "solmat_ne" ) = 0, ( "inputargs" ) = [(diff(u(r, t), r)+r*(diff(diff(u(r, t), r), r)))/r = diff(u(r, t), t), {u(1, t) = 0, u(4, t) = 0, u(r, 0) = r}], ( "multidep" ) = [false, false], ( "initialized" ) = false, ( "BCS", 1 ) = {[[1, 0, 1], b[1, 0, 1]], [[1, 0, 4], b[1, 0, 4]]}, ( "matrixhf" ) = true, ( "ICS" ) = [r], ( "timeadaptive" ) = false, ( "solspace" ) = Vector(21, {(1) = 1.0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = 4.0}, datatype = float[8]), ( "vectorproc" ) = proc (v, vp, vpp, t, x, k, h, n, vec) local _s1, _s2, _s3, _s4, _s5, _s6, xi; _s3 := -2*k; _s4 := -4*h^2; _s5 := -h*k; _s6 := 4*h^2*k; vec[1] := 0; vec[n] := 0; for xi from 2 to n-1 do _s1 := -vp[xi-1]+vp[xi+1]; _s2 := vp[xi-1]-2*vp[xi]+vp[xi+1]; vec[xi] := (_s2*_s3*x[xi]+_s4*vp[xi]*x[xi]+_s1*_s5)/(_s6*x[xi]) end do end proc, ( "solvec1" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0}, datatype = float[8]), ( "timeidx" ) = 2, ( "depvars" ) = [u], ( "bandwidth" ) = [1, 2], ( "depshift" ) = [1], ( "soltimes" ) = Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]), ( "timevar" ) = t, ( "solvec2" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0}, datatype = float[8]), ( "timestep" ) = .150000000000000, ( "spaceadaptive" ) = false, ( "solvec3" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0}, datatype = float[8]), ( "IBC" ) = b, ( "solmat_is" ) = 0, ( "errorest" ) = false, ( "mixed" ) = false, ( "vectorhf" ) = true, ( "linear" ) = true, ( "t0" ) = 0, ( "periodic" ) = false ] ); if xv = "left" then return INFO["solspace"][1] elif xv = "right" then return INFO["solspace"][INFO["spacepts"]] elif tv = "start" then return INFO["t0"] elif not (type(tv, 'numeric') and type(xv, 'numeric')) then error "non-numeric input" end if; if xv < INFO["solspace"][1] or INFO["solspace"][INFO["spacepts"]] < xv then error "requested %1 value must be in the range %2..%3", INFO["spacevar"], INFO["solspace"][1], INFO["solspace"][INFO["spacepts"]] end if; dary := Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]); daryt := 0; daryx := 0; dvars := []; errest := false; nd := nops(INFO["depvars"]); if dary[nd+1] <> tv then try `pdsolve/numeric/evolve_solution`(INFO, tv) catch: msg := StringTools:-FormatMessage(lastexception[2 .. -1]); if tv < INFO["t0"] then error cat("unable to compute solution for %1<%2:
", msg), INFO["timevar"], INFO["failtime"] else error cat("unable to compute solution for %1>%2:
", msg), INFO["timevar"], INFO["failtime"] end if end try end if; if dary[nd+1] <> tv or dary[nd+2] <> xv then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["solspace"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, dary); if errest then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_t"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryt); `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_x"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryx) end if end if; dary[nd+1] := tv; dary[nd+2] := xv; if dvars = [] then [seq(dary[i], i = 1 .. INFO["norigdepvars"])] else vals := NULL; for i to nops(dvars) do j := eval(dvars[i]); try if errest then vals := vals, evalhf(j(tv, xv, dary, daryt, daryx)) else vals := vals, evalhf(j(tv, xv, dary)) end if catch: userinfo(5, `pdsolve/numeric`, `evalhf failure`); try if errest then vals := vals, j(tv, xv, dary, daryt, daryx) else vals := vals, j(tv, xv, dary) end if catch: vals := vals, undefined end try end try end do; [vals] end if end proc; stype := "2nd"; if nargs = 1 then if args[1] = "left" then return solnproc(0, "left") elif args[1] = "right" then return solnproc(0, "right") elif args[1] = "start" then return solnproc("start", 0) else error "too few arguments to solution procedure" end if elif nargs = 2 then if stype = "1st" then tv := evalf(args[1]); xv := evalf(args[2]) else tv := evalf(args[2]); xv := evalf(args[1]) end if; if not (type(tv, 'numeric') and type(xv, 'numeric')) then if procname <> unknown then return ('procname')(args[1 .. nargs]) else ndsol := pointto(solnproc("soln_procedures")[1]); return ('ndsol')(args[1 .. nargs]) end if end if else error "incorrect arguments to solution procedure" end if; vals := solnproc(tv, xv); vals[1] end proc

(1)

eval(diff(sd(r, t), r), [r = 2, t = 4])

(D[1](sd))(2, 4)

(2)

subs(r = 2, t = 4, diff(sd(r, t), r))

diff(sd(2, 4), 2)

(3)

 Using numerical methods, I cannot calculate the derivative of sd with respect to r at r = 2 and t = 4.

Oliveira.

``


 

Download Derivative-numerical.mw

Does anyone know how to enter in the pdsolve function Dirichlet conditions and Neumann values?

Oliveira.

I am reading the help page for "time" and it says that it will display the time elapsed since the maple kernel was loaded, but I just want output that is the value of the time and date displayed on my computer at the point the input in the command line is exrcuted. How do I do this? 

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