Maple 18 Questions and Posts

These are Posts and Questions associated with the product, Maple 18

partial differential equation question??

utt = 9uxx

boundary conditions : u (0,t) = (2,t) = 0

initial conditions : u (x,0) = f(x) = { x(2-x)   ,0<x<1     ,      x   ,1<x<2  = 0 , t>0 ,

                         u(x,0) = 0 , 0<x<2

 

How to sketch 3D graph finite string problem of wave equation in partial differential equation using maple?

utt = 4uxx

boundary conditions : u (0,t) = (5,t) = 0 , t>0 ,

initial conditions : u (x,0) = f(x) = { 0, 0<x<4      , (5-x) , 4<x<5 

                         u(x,0) = 0 , 0<x<5

 

how to sketch 3D graph for solution of the corresponding partial differential equations ?? 

I'm trying to execute the linked code but i am having the following error:

Error, (in sombrea2) cannot determine if this expression is true or false: -(1/4)*105^(1/2) <= (1/4)*105^(1/2)
 

The entire procedure is downloadable here: http://www.mediafire.com/file/llcfhydpjy8tken/maple17.mw/file

If someone can help me to find a solution I'll be very thankful.

I have written the following commands in Maple 18.

implicit_func := x^3+y^3 = 9*x*y;
c := 2;
s := evalf(solve(subs(x = c, implicit_func)));
m1 := evalf(eval(implicitdiff(implicit_func, y, x), {x = c, y = s[1]}));
                          0.8000000000
m2 := evalf(eval(implicitdiff(implicit_func, y, x), {x = c, y = s[2]}));
                          -1.257321410
m3 := evalf(eval(implicitdiff(implicit_func, y, x), {x = c, y = s[3]}));
                          0.4573214099

How can I graph all "implicit_func, y - s[1] = m1*(x-c), y - s[2] = m2*(x-c), y - s[3] = m3*(x-c), and the points (c,s[1]), (c,s[2]), and (c,s[3])" in a plane? (Each of them in a different color)     

I am writting the following commands in Maple 18.

imp_fun := -4*x + 10*(x^2)*(y^(-2)) + y^2 =11: c := 2: s := evalf( solve( subs( x = c, imp_fun))): m1 := evalf( subs ( { x = c, y = s[1] }, implicitdiff( imp_fun, y,x)));

Now I expect to see a value for m1 but I see again the last command in blue.

Could you please help me to see the value for m1 by writting these commands?

restart;
M := -6*alpha*eta^2*mu*(lambda^2*mu+1)/`&vartheta;`+12*alpha*eta^2*lambda*mu^(3/2)*(sqrt(mu)*cot(A+sqrt(mu)*eta*(-t*(-alpha*eta^2*mu+f)+x))*lambda+1)/(`&vartheta;`*cot(A+sqrt(mu)*eta*(-t*(-alpha*eta^2*mu+f)+x)))-6*alpha*eta^2*mu*(sqrt(mu)*cot(A+sqrt(mu)*eta*(-t*(-alpha*eta^2*mu+f)+x))*lambda+1)^2/(`&vartheta;`*cot(A+sqrt(mu)*eta*(-t*(-alpha*eta^2*mu+f)+x))^2)+6*mu*eta^2*alpha*sqrt(sigma*(1+cot(A+sqrt(mu)*eta*(-t*(-alpha*eta^2*mu+f)+x))^2))/(sqrt(sigma)*theta*cot(A+sqrt(mu)*eta*(-t*(-alpha*eta^2*mu+f)+x))^2);
             2    /      2       \   
  6 alpha eta  mu \lambda  mu + 1/   
- -------------------------------- + 
             &vartheta;              

                                1                               
  ------------------------------------------------------------- 
                /      (1/2)     /   /          2       \    \\ 
  &vartheta; cot\A + mu      eta \-t \-alpha eta  mu + f/ + x// 

  /            2          (3/2) /  (1/2)    / 
  \12 alpha eta  lambda mu      \mu      cot\A

       (1/2)     /   /          2       \    \\           \\   
   + mu      eta \-t \-alpha eta  mu + f/ + x// lambda + 1// - 

                                1                                
  -------------------------------------------------------------- 
                                                               2 
                /      (1/2)     /   /          2       \    \\  
  &vartheta; cot\A + mu      eta \-t \-alpha eta  mu + f/ + x//  

  /           2    /  (1/2)    / 
  \6 alpha eta  mu \mu      cot\A

       (1/2)     /   /          2       \    \\           \  \   
   + mu      eta \-t \-alpha eta  mu + f/ + x// lambda + 1/^2/ + 

  /                /      / 
  |        2       |      | 
  \6 mu eta  alpha \sigma \1

                                                       2\\      \/
        /      (1/2)     /   /          2       \    \\ ||      | 
   + cot\A + mu      eta \-t \-alpha eta  mu + f/ + x// //^(1/2)/ 

  /                 
  |     (1/2)       
  \sigma      theta 

                                                    2\
     /      (1/2)     /   /          2       \    \\ |
  cot\A + mu      eta \-t \-alpha eta  mu + f/ + x// /
alpha := 2;
                               2
eta := 3;
                               3
mu := 1.5;
                              1.5
lambda := 2;
                               2
theta := 3;
                               3
sigma := .5;
                              0.5
b := .5;
                              0.5
f := 5;
                               5
y := 0;
                               0
plot3d([abs(M)], x = -3 .. 3, t = -3 .. 3);
 

general_solution.mwI want to calculate the diff equations numerical solutions at z=500 with calling the integrals with limits -500..Z and i want the datefile of resualts

 

i am currently using Maple 18, i have a problem on inserting 12 row by 12 column matrix and above is seem to be impossible. please can help or direct me on how to insert 12 row by 12 column matrix in maple. because my maple 18 seem to stop in 10 row by 10 column matrix.  thanks

restart;
Digits := 15;

b := -I;

a := sqrt(2);

epsilon := 1;

f := proc (t) options operator, arrow; evalf(Int(exp(I*k*t)/((1+a^2*sin(k)^2)*(k-b)^epsilon), k = -infinity .. infinity)) end proc;

f(1.3)

 

I tried different methods like _d01amc, but either I have this error:

Error, (in evalf/int) NE_QUAD_NO_CONV:
  The integral is probably divergent or slowly convergent.


or it takes forever.

I also tried to map the interval to some finite length (k=tan(u)), but then I get

Error, (in evalf/int) NE_QUAD_BAD_SUBDIV:
  Extremely bad integrand behaviour occurs around the
  sub-interval (-1,5707963e+000, -1,5707963e+000 ).


disgusting integrand?

Hi

I would like to solve the integrodifferential equation and then look to the  stability of the origin.

Is it  stable, uniformly stable, asymptotically stable and uniformly asumptotically stable.

Please see the following code.

Code.mw

Thanks

 

 

restart;

Digits := 32;

t0 := 1;

eq := 1-w*v^2-2*v*exp(-t/v);

equ := eval(eq, v = -t/ln(u));

us := solve(eval(equ, t = t0), u);

vs := -t0/ln(us);

plot(Re(vs), w = 0 .. 10, view = 0 .. 1)

 

 

I want to plot the solution of this equation, but it doesn't quite work. I tried to transform it, because I thought the singularity in the denominator of the exponential causes the issues.

any suggestions?

Hello,

I'm wondering which connection formulas maple has access to?

For instance consider the following exmple

restart;

hypergeom([a, b], [c], 1);

`assuming`([convert(%, GAMMA)], [c-a-b > 0])

 

it should be simplified to GAMMA functions, but I do not get maple to do it. Are there packages for this?

 

Same for higher functions pFq for example

hypergeom([1, 1, 2*q-2+L], [2, L+1], 1)

under appropriate assumptions.

This is a follow up question to https://mapleprimes.com/questions/225877-Partial-Integration-Hint:

restart;

with(Physics, KroneckerDelta);

Digits := 15;

t4 := 1/3;

n := 4;

q := 4/7;

i1 := evalf(Int(t^n*exp(-t)*GAMMA(2*q-2, t*(1-t4)*(1/t4)), t = 0 .. infinity, method = _d01amc));

i2 := expand(simplify(GAMMA(2*q-2)*add(binomial(n, m)*(KroneckerDelta[m, 0]-GAMMA(3-2*q)*(1/GAMMA(3-2*q-m))*t4^m*(1-t4)^(2*q-2))*(-1)^m*factorial(n-m), m = 0 .. n)));

`~`[evalf]([op(i2)]);

add(%);

i3 := expand(simplify(eval((-1)^n*GAMMA(2*q-2)*(diff((1-(1+t4*x*(1/(1-t4)))^(2-2*q))*(1/x), x$n)), x = 1)));

`~`[evalf]([op(i3)]);

add(%)

 

Interestingly this works up to n=3. It seems that the second term is wrongly manipulated and it should be 168/6 instead of 175/6?

 

I doubt the derivatives are wrong since I checked individually. I also hardly doubt this is a numerical round off, as the discrepancy is too large.

Is this a bug, or is there actually an error?

How do I remove infinity from a list

s:=[f(x) , exp(a), GAMMA(2x)-1 , infinity , 1, -infinity]

remove(has,%,infinity)

does not work.

It should yield

s:=[f(x) , exp(a), GAMMA(2x)-1 , 1]

Hello, I am getting the following output from maple: (-ln(lambda)-gamma-ln(k+b))/(k+b) . I have all variables (lambda, k, b) but not gamma and I am not sure what actually it is. I believe it is some kind of Gamma function but I cannot find any expressions for that. Ussually for gamma function I get something like GAMMA(x). Does someone know what this lower case gamma is?

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