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need help with the code...

Asked by: kristavaldes 15
homework fibonacci
July 19 2018
0  0


If n people (numbered 1 to n) stand in a circle and someone starts going around the circle and eliminating every other person till only one person is left, the number J(n) of the person left at the end is given by 

    J(n) = 1                           if n = 1
    J(n) = 2*J(n/2) - 1          if n > 1 and n is even
    J(n) = 2*J((n-1)/2) + 1   if  n > 1 and n is odd

(i) Write a recursive procedure to compute J. [As a check the first 16 values (starting with 1) of J(n) are 1,1,3,1,3,5,7,1,3,5,7,9,11,13,15,1]. 
(ii)Compute the value of J(10000). 
(iii) Can you explain why this is so much faster than our recursive procedure to compute the n-th Fibonacci number?

Anyone successfully installed/run Maple in ubuntu ...

Asked by: reid 10
July 19 2018
2  4

Has anyone installed and run maple under ubuntu installed the Windows Subsystem for Linux?   We are having trouble doing this: specifically running programs with text input files, etc.

 

 

Why does the summation not work?...

Asked by: Ronan 1341
sum
July 18 2018
0  1

I have a say sum(F(k) ,k=1..n)  It fails unless n is an actual integer.  But sum(F(k), k=1..a) works. Then then eval(%,a=n) completes it. That is probably correct but not necessarily a valid assumption. Details in attached. Also it is hard to understand the error message.
 

restart

``

``

Sinta := (k^2+n^2-k)*n/((k^2+n^2-2*k+1)*(k^2+n^2))

(k^2+n^2-k)*n/((k^2+n^2-2*k+1)*(k^2+n^2))

 (1)

Ai := sum(Sinta, k = 1 .. n)

-((1/2)*I)*(2*n^2+I*n)*Psi(n-I*n)/(4*n^2+1)+((1/2)*I)*(2*n^2-I*n)*Psi(n+I*n)/(4*n^2+1)+((1/2)*I)*(-2*n^2+I*n)*Psi(n+1-I*n)/(4*n^2+1)-((1/2)*I)*(-2*n^2-I*n)*Psi(n+1+I*n)/(4*n^2+1)+((1/2)*I)*(2*n^2+I*n)*Psi(-I*n)/(4*n^2+1)-((1/2)*I)*(2*n^2-I*n)*Psi(I*n)/(4*n^2+1)-((1/2)*I)*(-2*n^2+I*n)*Psi(1-I*n)/(4*n^2+1)+((1/2)*I)*(-2*n^2-I*n)*Psi(1+I*n)/(4*n^2+1)

 (2)

Souta := n/(k^2+n^2-k)

n/(k^2+n^2-k)

 (3)

NULL

sum(Souta, k = 1 .. n)

Error, (in assuming) when calling 'Dfnt_4'. Received: 'when calling 'Dfnt_4'. Received: 'when calling 'unknown'. Received: 'invalid input: Dfnt_4 expects its 3rd argument, fpts, to be of type Or(list, piecewise), but received 0'''

  

"(->)"

Error, invalid input: evalf[10] expects 1 argument, but received 0

  

 

 

This works

sum(Souta, k = 1 .. a)

n*Psi(a+1/2-(1/2)*(-4*n^2+1)^(1/2))/(-4*n^2+1)^(1/2)-n*Psi(a+1/2+(1/2)*(-4*n^2+1)^(1/2))/(-4*n^2+1)^(1/2)-n*Psi(1/2-(1/2)*(-4*n^2+1)^(1/2))/(-4*n^2+1)^(1/2)+n*Psi(1/2+(1/2)*(-4*n^2+1)^(1/2))/(-4*n^2+1)^(1/2)

 (4)

Ao := eval(%, a = n)

n*Psi(n+1/2-(1/2)*(-4*n^2+1)^(1/2))/(-4*n^2+1)^(1/2)-n*Psi(n+1/2+(1/2)*(-4*n^2+1)^(1/2))/(-4*n^2+1)^(1/2)-n*Psi(1/2-(1/2)*(-4*n^2+1)^(1/2))/(-4*n^2+1)^(1/2)+n*Psi(1/2+(1/2)*(-4*n^2+1)^(1/2))/(-4*n^2+1)^(1/2)

 (5)

"(->)"

n*Psi(n+.5000000000-.5000000000*(-4.*n^2+1.)^(1/2))/(-4.*n^2+1.)^(1/2)-1.*n*Psi(n+.5000000000+.5000000000*(-4.*n^2+1.)^(1/2))/(-4.*n^2+1.)^(1/2)-1.*n*Psi(.5000000000-.5000000000*(-4.*n^2+1.)^(1/2))/(-4.*n^2+1.)^(1/2)+n*Psi(.5000000000+.5000000000*(-4.*n^2+1.)^(1/2))/(-4.*n^2+1.)^(1/2)

 (6)

````

``


 

Download Summation_problem.mw

Problem in comparing the coefficient from an exres...

Asked by: Muhammad Usman 245
coeff
July 17 2018
0  1

Dear Users!

Hope you would be fine. I want to construct system of equations by comparing the likes powers of x^i*y^j*t^k1*exp(k2*eta) for an expression H1 present in attached file. Please see the fix my problem. I shall be very thankful for your kind help. 

Help.mw

Can I turn off warning sound?...

Asked by: peter2108 95
sound
July 16 2018
2  4

From  time to tiime Malel emits a sort of "Boiing" noise when I make a keyboard error. I am not sure exaclty when it does this, but it is loud. Is it possible to turn it off? I have looked quite extensively and cannot find out anything.

sum not converging...

Asked by: radaar 202
sum convergence
July 14 2018
0  10

In the following problem at two example are given. For Z=2 the sum is converging whereas at Z=4 it is not converging. Thank you

 

PROBLEM.mw

How do I obtain a numerical solution of a nonlinea...

Asked by: isifesai 30
numeric integral-equation
July 13 2018
0  5

I have a problem writing a program for the numerical solution of nonlinear volterra integral equation using the method of reproducing kernel space. I have my algorithm as well as the program I tried to write, though they are full of error messages. Please could anyone give me a clue on how to go about my challenges. The algorithm is as follows:

Step 1. Fix 𝑎 ≤ 𝑥 and 𝑡 ≤ 𝑏.
If 𝑡 ≤ 𝑥, set 𝑅𝑥(𝑡) = 1 − 𝑎 + 𝑡.
Else set 𝑅𝑥(𝑡) = 1 − 𝑎 + 𝑥.
Step 2. For 𝑖 = 1, 2, . . . , 𝑚 set 𝑥i = (𝑖 − 1)/(𝑚 − 1).

Set 𝜓i(𝑥) = 𝐿t𝑅𝑥(𝑡)|𝑡=𝑥i .
Step 3. Set 𝑢0(𝑥1) = 𝑢(𝑥1).
Step 4. For 𝑖 = 1, 2, . . . , 𝑚 set 𝛾ij = [𝜓-1]ij.
Step 5. 𝑛 = 1.
Step 6. Set Sn = Σ𝑛
𝑘=1 𝛾nk𝑢k-1(𝑥k).
Step 7. Set 𝑢n(𝑥) = Σ𝑛
𝑖=1 Si𝜓i(𝑥).
Step 8. If 𝑛 < 𝑚then set 𝑛 = 𝑛 + 1 and go to step 6.
Else stop.

Expression not correct? Solving a system of equati...

Asked by: digerdiga 390
limit series
July 13 2018
0  3

So I have this system of equations with which I am not sure if the result is the same or not using "series" and "limit" or what is going on here.

I hope it is clear what I mean.


 

> 

restart; with(MathematicalFunctions); Assume(k__2H2O > 0, `k__HA+OH` > 0, `k__A+H2O` > 0, `k__H3O+OH` > 0, `k__HA+H2O` > 0, `k__H3O+A` > 0, HA__0 > 0, H2O > 0); sys := k__2H2O*H2O^2+`k__A+H2O`*H2O*(HA__0-HA)-(H3O*`k__H3O+OH`+HA*`k__HA+OH`)*OH = 0, k__2H2O*H2O^2+`k__HA+H2O`*H2O*HA-(`k__H3O+A`*(HA__0-HA)+`k__H3O+OH`*OH)*H3O = 0, (H2O*`k__HA+H2O`+OH*`k__HA+OH`)*HA-(H2O*`k__A+H2O`+H3O*`k__H3O+A`)*(HA__0-HA) = 0; sys := `~`[simplify]([eval(eval(sys, HA = HA__0+OH-H3O), HA__0 = x__HA0*H2O)]); sol := solve(sys, [OH, H3O]); sol := sol[1]; OH__sol := simplify(rhs(sol[1])); H3O__sol := simplify(rhs(sol[2])); simplify(OH__sol*H3O__sol); OHH3O := simplify(limit(%, `k__HA+OH` = 0)); series(OHH3O, x__HA0 = 0, 2); collect(convert(%, polynom), x__HA0, simplify, factor); r1 := limit(%, x__HA0 = 0); r2 := radnormal(limit(OHH3O, x__HA0 = 0)); simplify(r1-r2)

[`&Intersect`, `&Minus`, `&Union`, Assume, Coulditbe, Evalf, Get, Is, SearchFunction, Sequences, Series]

  

{H2O::(RealRange(Open(0), infinity))}, {HA__0::(RealRange(Open(0), infinity))}, {k__2H2O::(RealRange(Open(0), infinity))}, {`k__A+H2O`::(RealRange(Open(0), infinity))}, {`k__H3O+A`::(RealRange(Open(0), infinity))}, {`k__H3O+OH`::(RealRange(Open(0), infinity))}, {`k__HA+H2O`::(RealRange(Open(0), infinity))}, {`k__HA+OH`::(RealRange(Open(0), infinity))}

  

k__2H2O*H2O^2+`k__A+H2O`*H2O*(HA__0-HA)-(H3O*`k__H3O+OH`+HA*`k__HA+OH`)*OH = 0, k__2H2O*H2O^2+`k__HA+H2O`*H2O*HA-(`k__H3O+A`*(HA__0-HA)+`k__H3O+OH`*OH)*H3O = 0, (H2O*`k__HA+H2O`+OH*`k__HA+OH`)*HA-(H2O*`k__A+H2O`+H3O*`k__H3O+A`)*(HA__0-HA) = 0

  

[-OH^2*`k__HA+OH`+((-x__HA0*`k__HA+OH`-`k__A+H2O`)*H2O+H3O*(`k__HA+OH`-`k__H3O+OH`))*OH+k__2H2O*H2O^2+`k__A+H2O`*H2O*H3O = 0, (x__HA0*`k__HA+H2O`+k__2H2O)*H2O^2+`k__HA+H2O`*(OH-H3O)*H2O+(-`k__H3O+A`*H3O+OH*(`k__H3O+A`-`k__H3O+OH`))*H3O = 0, H2O^2*x__HA0*`k__HA+H2O`+((x__HA0*`k__HA+OH`+`k__A+H2O`+`k__HA+H2O`)*OH-H3O*(`k__A+H2O`+`k__HA+H2O`))*H2O+(OH-H3O)*(H3O*`k__H3O+A`+OH*`k__HA+OH`) = 0]

  

-RootOf(-x__HA0*`k__A+H2O`^2*`k__HA+H2O`+k__2H2O^2*`k__H3O+A`-k__2H2O*`k__A+H2O`^2-k__2H2O*`k__A+H2O`*`k__HA+H2O`+(2*x__HA0*`k__A+H2O`*`k__H3O+OH`*`k__HA+H2O`-k__2H2O*`k__A+H2O`*`k__H3O+A`+k__2H2O*`k__A+H2O`*`k__H3O+OH`+k__2H2O*`k__H3O+OH`*`k__HA+H2O`)*_Z+(-x__HA0*`k__H3O+OH`^2*`k__HA+H2O`-k__2H2O*`k__H3O+A`*`k__H3O+OH`+`k__A+H2O`^2*`k__H3O+OH`+`k__A+H2O`*`k__H3O+OH`*`k__HA+H2O`)*_Z^2+(`k__A+H2O`*`k__H3O+A`*`k__H3O+OH`-`k__A+H2O`*`k__H3O+OH`^2-`k__H3O+OH`^2*`k__HA+H2O`)*_Z^3)*H2O^2*(-`k__A+H2O`*RootOf(-x__HA0*`k__A+H2O`^2*`k__HA+H2O`+k__2H2O^2*`k__H3O+A`-k__2H2O*`k__A+H2O`^2-k__2H2O*`k__A+H2O`*`k__HA+H2O`+(2*x__HA0*`k__A+H2O`*`k__H3O+OH`*`k__HA+H2O`-k__2H2O*`k__A+H2O`*`k__H3O+A`+k__2H2O*`k__A+H2O`*`k__H3O+OH`+k__2H2O*`k__H3O+OH`*`k__HA+H2O`)*_Z+(-x__HA0*`k__H3O+OH`^2*`k__HA+H2O`-k__2H2O*`k__H3O+A`*`k__H3O+OH`+`k__A+H2O`^2*`k__H3O+OH`+`k__A+H2O`*`k__H3O+OH`*`k__HA+H2O`)*_Z^2+(`k__A+H2O`*`k__H3O+A`*`k__H3O+OH`-`k__A+H2O`*`k__H3O+OH`^2-`k__H3O+OH`^2*`k__HA+H2O`)*_Z^3)+k__2H2O)/(-`k__H3O+OH`*RootOf(-x__HA0*`k__A+H2O`^2*`k__HA+H2O`+k__2H2O^2*`k__H3O+A`-k__2H2O*`k__A+H2O`^2-k__2H2O*`k__A+H2O`*`k__HA+H2O`+(2*x__HA0*`k__A+H2O`*`k__H3O+OH`*`k__HA+H2O`-k__2H2O*`k__A+H2O`*`k__H3O+A`+k__2H2O*`k__A+H2O`*`k__H3O+OH`+k__2H2O*`k__H3O+OH`*`k__HA+H2O`)*_Z+(-x__HA0*`k__H3O+OH`^2*`k__HA+H2O`-k__2H2O*`k__H3O+A`*`k__H3O+OH`+`k__A+H2O`^2*`k__H3O+OH`+`k__A+H2O`*`k__H3O+OH`*`k__HA+H2O`)*_Z^2+(`k__A+H2O`*`k__H3O+A`*`k__H3O+OH`-`k__A+H2O`*`k__H3O+OH`^2-`k__H3O+OH`^2*`k__HA+H2O`)*_Z^3)+`k__A+H2O`)

  

-(k__2H2O*`k__H3O+A`^2-2*`k__A+H2O`^2*`k__H3O+A`+`k__A+H2O`^2*`k__H3O+OH`-2*`k__A+H2O`*`k__H3O+A`*`k__HA+H2O`+2*`k__A+H2O`*`k__H3O+OH`*`k__HA+H2O`+`k__H3O+OH`*`k__HA+H2O`^2)*`k__A+H2O`*`k__HA+H2O`*H2O^2*x__HA0/((`k__A+H2O`*`k__H3O+A`-`k__A+H2O`*`k__H3O+OH`-`k__H3O+OH`*`k__HA+H2O`)*(k__2H2O*`k__H3O+A`^2-`k__A+H2O`^2*`k__H3O+OH`-2*`k__A+H2O`*`k__H3O+OH`*`k__HA+H2O`-`k__H3O+OH`*`k__HA+H2O`^2))-(k__2H2O*`k__H3O+A`-`k__A+H2O`^2-`k__A+H2O`*`k__HA+H2O`)*H2O^2*(`k__A+H2O`+`k__HA+H2O`)/(`k__H3O+A`*(`k__A+H2O`*`k__H3O+A`-`k__A+H2O`*`k__H3O+OH`-`k__H3O+OH`*`k__HA+H2O`))

  

-(k__2H2O*`k__H3O+A`-`k__A+H2O`^2-`k__A+H2O`*`k__HA+H2O`)*H2O^2*(`k__A+H2O`+`k__HA+H2O`)/(`k__H3O+A`*(`k__A+H2O`*`k__H3O+A`-`k__A+H2O`*`k__H3O+OH`-`k__H3O+OH`*`k__HA+H2O`))

  

k__2H2O*H2O^2/`k__H3O+OH`

  

-`k__A+H2O`*(-(`k__A+H2O`+`k__HA+H2O`)^2*`k__H3O+OH`+k__2H2O*`k__H3O+A`^2)*H2O^2/(`k__H3O+OH`*`k__H3O+A`*((-`k__A+H2O`-`k__HA+H2O`)*`k__H3O+OH`+`k__A+H2O`*`k__H3O+A`))

 (1)
> 

``


 

Download Mapleprimes_-_Ionproduct.mw

is there example data that can verify maxwell equa...

Asked by: LeeHoYeung 535
physics
July 08 2018
0  0

is there example data that can verify maxwell equations?

How to calculate determinant of a cube matrix ?...

Asked by: LeeHoYeung 535
tensor determinant
July 08 2018
0  2

How to calculate determinant of a cube matrix ?

is there function to calculate 3x 3x 3 cube determinant?

How to proof classical and quantum both p summatio...

Asked by: LeeHoYeung 535
July 07 2018
0  0

How to proof classical and quantum both p summation equal to one in maple?

solve these partial differential equations via p...

Asked by: 9009134 110
pde pdsolve differential-equations
July 06 2018
0  6

is possible to solve these partial differential equations in maple via pdsolve?

Thanks

An amusing bug(ette)...

Asked by: tomleslie 13876
input 2dmath range
July 05 2018
1  6

In an unrelated thread, I provided the OP with some 1-D code, which contained the Array definition

TC:= Array(0...1001, fill=0)

Note the existence of three '.' characters in the range specification. This was a typo on my part, or my '.' key bounced, or something. The code containing the above definition "worked" with no problem, which, presumably, was why I didn't notice.

The Maple help does state (my emphasis)

Note that more than two dots in succession are also parsed as the range (..) operator.

although I wasn't making use of this fact - I just screwed up when typing the original.

The OP preferred to use 2-D input, and used cut-and-paste to transfer the above code, resulting in 2-D input, which is where the fun started. It seems(?) that when using 2-D input, more than two dots in succession is only interpreted as a straightforward range, if the total number of dots is even.

If the total number of dots is odd, then it appears(?) as if the 'final' dot is associated with the second number in the range as a 'decimal point', (so producing .1001 in the above example). This is then 'coerced/rounded' to an integer - ie it becomes '0', and the above Array definition is interpreted as

TC:= Array(0..0, fill=0)

Consequences in the following code are left to your imagination

Worth an SCR?

 

 

 

how we can substitute the c1, c2,c3,c4,c5 in expre...

Asked by: hitecwaseem 15
eval substitution subs
July 04 2018
0  1

K := simplify(C, 'size');
      5                                                  4   
lambda  + (-a__11 - a__33 - a__44 - a__55 - a__22) lambda  + 

  ((a__44 + a__33 + a__22 + a__11) a__55

   + a__44 (a__33 + a__22 + a__11) + (a__33 + a__22) a__11

                                      3                    
   + a__33 a__22 - a__32 a__23) lambda  + (((-a__33 - a__22

   - a__11) a__44 + (-a__33 - a__22) a__11 - a__33 a__22

   + a__32 a__23) a__55

   + ((-a__33 - a__22) a__11 - a__33 a__22 + a__32 a__23) a__44

   + (-a__22 a__33 + a__23 a__32) a__11

                                              2            
   - a__32 (a__13 a__21 + a__24 a__43)) lambda  + ((((a__33

   + a__22) a__11 + a__33 a__22 - a__32 a__23) a__44

   + (a__22 a__33 - a__23 a__32) a__11

   + a__32 (a__13 a__21 + a__24 a__43)) a__55

   + ((a__22 a__33 - a__23 a__32) a__11 + a__13 a__21 a__32) a__44

   + a__32 (a__11 a__43 a__24 - a__21 (a__14 a__43 + a__15 a__53)

  )) lambda + (((-a__22 a__33 + a__23 a__32) a__11

   - a__13 a__21 a__32) a__44

   - a__43 a__32 (a__11 a__24 - a__14 a__21)) a__55

   - a__15 a__21 a__32 (a__43 a__54 - a__44 a__53)

u := [coeffs(K, [lambda], 'l')];
[(((-a__22 a__33 + a__23 a__32) a__11 - a__13 a__21 a__32) a__44

   - a__43 a__32 (a__11 a__24 - a__14 a__21)) a__55

   - a__15 a__21 a__32 (a__43 a__54 - a__44 a__53), 1, 

  -a__11 - a__33 - a__44 - a__55 - a__22, (a__44 + a__33 + a__22

   + a__11) a__55 + a__44 (a__33 + a__22 + a__11)

   + (a__33 + a__22) a__11 + a__33 a__22 - a__32 a__23, ((-a__33

   - a__22 - a__11) a__44 + (-a__33 - a__22) a__11 - a__33 a__22

   + a__32 a__23) a__55

   + ((-a__33 - a__22) a__11 - a__33 a__22 + a__32 a__23) a__44

   + (-a__22 a__33 + a__23 a__32) a__11

   - a__32 (a__13 a__21 + a__24 a__43), (((a__33 + a__22) a__11

   + a__33 a__22 - a__32 a__23) a__44

   + (a__22 a__33 - a__23 a__32) a__11

   + a__32 (a__13 a__21 + a__24 a__43)) a__55

   + ((a__22 a__33 - a__23 a__32) a__11 + a__13 a__21 a__32) a__44

   + a__32 (a__11 a__43 a__24 - a__21 (a__14 a__43 + a__15 a__53)

  )]
u[1] = C__5;
(((-a__22 a__33 + a__23 a__32) a__11 - a__13 a__21 a__32) a__44

   - a__43 a__32 (a__11 a__24 - a__14 a__21)) a__55

   - a__15 a__21 a__32 (a__43 a__54 - a__44 a__53) = C__5
C__1 = u[3];
         C__1 = -a__11 - a__33 - a__44 - a__55 - a__22
C__2 = u[4];
   C__2 = (a__44 + a__33 + a__22 + a__11) a__55

      + a__44 (a__33 + a__22 + a__11) + (a__33 + a__22) a__11

      + a__33 a__22 - a__32 a__23
C__3 = u[5];
C__3 = ((-a__33 - a__22 - a__11) a__44 + (-a__33 - a__22) a__11

   - a__33 a__22 + a__32 a__23) a__55

   + ((-a__33 - a__22) a__11 - a__33 a__22 + a__32 a__23) a__44

   + (-a__22 a__33 + a__23 a__32) a__11

   - a__32 (a__13 a__21 + a__24 a__43)
C__4 = u[6];
C__4 = (((a__33 + a__22) a__11 + a__33 a__22 - a__32 a__23) a__44

   + (a__22 a__33 - a__23 a__32) a__11

   + a__32 (a__13 a__21 + a__24 a__43)) a__55

   + ((a__22 a__33 - a__23 a__32) a__11 + a__13 a__21 a__32) a__44

   + a__32 (a__11 a__43 a__24 - a__21 (a__14 a__43 + a__15 a__53)

  )
 

How do we solve a diffusion equation with an integ...

Asked by: ibndirac 5
pde numeric differential-equations
July 03 2018
1  8

I am trying to solve a diffusion equation with a potential term that has an integral in it. The equation has the following form: 

PDE := diff(g(x, t), t) = diff((beta(x, t)+diff(g(x, t), x)), x), 

with the function beta: 

beta := proc (x, t) options operator, arrow; int(exp(-abs(x-y))*g(y, t), y = -infinity .. +infinity) end proc

The boundary conditions for the function g(x,t) are simply assumed to be a zero-centered Gaussian in space (i.e. in x). So it is unity for x=0 and zero for the outer boundary that we can set as x=L. 

The problem is easily solved if the function beta is not an integral, but in the current form I get the following error: 
*******
Error, (in pdsolve/numeric/process_PDEs) inconsistent dependencies in PDEs: g(x, t) v.s. g(y, t)

*******

So it does not like the dummy variable in the function g.  

I can not write an additional PDE for beta because my Kernel is an exponential so the integral never goes away. Anyone with a way to solve this?

ADDENDUM: I have now copied the scriptPDE_DIFFUSION_INTEGRAL.mw
 

> 

restart
> 

L := 20; betaz := proc (x, t) options operator, arrow; int(exp(-abs(x-y))*g(y, t), y = 0 .. L) end proc

proc (x, t) options operator, arrow; int(exp(-abs(x-y))*g(y, t), y = 0 .. L) end proc

 (1)
> 

PDE := diff(g(x, t), t) = diff(-betaz(x, t)+diff(g(x, t), x), x)

diff(g(x, t), t) = -(int(-abs(1, x-y)*exp(-abs(x-y))*g(y, t), y = 0 .. 20))+diff(diff(g(x, t), x), x)

 (2)
> 

v__t := 1; v__d := 0; IBC := {g(0, t) = exp(-(0.-v__d)^2/v__t), g(L, t) = 0*exp(-(L-v__d)^2/v__t), g(x, 0) = exp(-(x-v__d)^2/v__t)}

{g(0, t) = 1., g(20, t) = 0, g(x, 0) = exp(-x^2)}

 (3)
> 

pds := pdsolve(PDE, IBC, numeric, time = 100, range = 0 .. L, spacestep = .1)

Error, (in pdsolve/numeric/process_PDEs) inconsistent dependencies in PDEs: g(x, t) v.s. g(y, t)

  
> 

p0 := pds:-plot(t = 0, numpoints = 100, color = red); p1 := pds:-plot(t = 10, numpoints = 100, color = red); p2 := pds:-plot(t = 20, numpoints = 100, color = blue); p6 := pds:-plot(t = 60, numpoints = 100, color = blue); p5 := pds:-plot(t = 50, numpoints = 100, color = blue); p3 := pds:-plot(t = 30, numpoints = 100, color = blue); p4 := pds:-plot(t = 40, numpoints = 100, color = green); p7 := pds:-plot(t = 70, numpoints = 100, color = blue); p8 := pds:-plot(t = 80, numpoints = 100, color = black); p9 := pds:-plot(t = 90, numpoints = 100, color = blue); plots[display]({p0, p2, p4, p8})
> 

NULL


 

Download PDE_DIFFUSION_INTEGRAL.mw

below. 

 
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