Maple 2015 Questions and Posts

These are Posts and Questions associated with the product, Maple 2015

Dearz!

Hope everyone is fine with everything. I am facing problem to solve the system of PDEs in the attached file. Is there any built-in command to the solve the attached system of PDEs via FEM, FDM, SIMPLER algorithm or some other efficient method? Please try to fix my problem. I am waiting your positive response. Thanks in advance.

PDEs_sol.mw

Hello,

Could you please help me with the following problem? I'm new to Maple and i need some help.

Solve the equation x^3 - a*x + 1 = 0 , in x. Determine the particular solution for a=1,2,... .Graphically represent the polynom that appears in the equation, in a case where the equation has a real root and in a case where the equation has 3 real roots.

Thank you !

Hi everibody 

I work with Maple 2015 under OS-X El Capitan.

Using more than one matrix vector product (either M.V  or MatrixVectorMultiply(M,V)  ; M is a n by p matrix and V a column vector of size p) within the same block of commands generates an error.

Do other people have the same problem ?
Thanks for your feedback.

SomethingGoesWrong.mw


PS : I know I can do this   X . <<1, 1, -1> | <-1, 2, 0>> but this doesn't explain the error I get

 

what are the dynamical system which act on invariant manifold?

Hi,

This sequence of commands works perfectly well

     plotsetup(jpeg, plotoutput=SomeJpegFile);
     plot(x, x=0..1);
     plotsetup(default);


Why this one doesn't create the file SomeJpegFile ?

f := proc()
     plotsetup(jpeg, plotoutput=SomeJpegFile);
     plot(x, x=0..1);
     plotsetup(default);
end proc;

f();


Thanks in advance

Is it a complete set ? How to search matrix?

Dear 

Hope everyone is good. I am face to attaine the converges solution of the attached problem. Please have a look and fix my problem. I am waiting your response

diverges.mw


 

لا شيء

-------------------------------------------------- -------------------------------------------------- -------------------------------------------------- -------------------------

إعادة بدء

مع (LinearAlgebra)

مع (orthopoly)

مع (طالب)

لا شيء

لا شيء

لا شيء

لا شيء

سيل (ألفا): = 2؛  سيل (بيتا): = 1؛  ألفا: = 1.5؛  بيتا: = .5

2

 

1

 

1.5

 

0.5

(1)

n: = 8؛  m: = 8

8

 

8

(2)

 

لا شيء

x [3]: = .611423302089630؛  x [4]: ​​= 1.09446605083631؛  x [5]: = 1.99636816302962؛  x [6]: = 3.38757178455234؛  x [7]: = 5.41873370919121؛  x [8]: = 8.49143699030089

،611423302089630

 

+1.09446605083631

 

1.99636816302962

 

3.38757178455234

 

5.41873370919121

 

8.49143699030089

(3)

# 1 / حساب مصفوفة (A). (طريقة الجمع)

A := array(1 .. n, 1 .. m); for j to m do A[1, j] := evalf(subs(x = 0, L(j-1, 2*x-1))) end do; for j to m do A[2, j] := evalf(subs(x = 0, diff(L(j-1, 2*x-1), x))) end do; for i from 3 to n do for j to m do A[i, j] := evalf(subs(x = x[i], fracdiff(L(j-1, 2*x-1), x, alpha, method = direct))+subs(x = x[i], fracdiff(L(j-1, 2*x-1), x, beta, method = direct))+subs(x = x[i], diff(L(j-1, 2*x-1), x))+subs(x = x[i], L(j-1, 2*x-1))) end do end do

print(`A=`, A)

`A=`, A

(4)

A := convert(A, Matrix)

A := Matrix(8, 8, {(1, 1) = 1., (1, 2) = 2., (1, 3) = 3.500000000, (1, 4) = 5.666666667, (1, 5) = 8.708333333, (1, 6) = 12.88333333, (1, 7) = 18.50972222, (1, 8) = 25.97658730, (2, 1) = 0., (2, 2) = -2., (2, 3) = -6., (2, 4) = -13., (2, 5) = -24.33333333, (2, 6) = -41.75000000, (2, 7) = -67.51666667, (2, 8) = -104.5361111, (3, 1) = 1., (3, 2) = -2.987486314, (3, 3) = -3.301220288, (3, 4) = .5119939327, (3, 5) = 9.171314221, (3, 6) = 23.72035697, (3, 7) = 45.59773916, (3, 8) = 76.72165628, (4, 1) = 1., (4, 2) = -4.549878909, (4, 3) = -1.208865530, (4, 4) = 6.408882482, (4, 5) = 16.03540544, (4, 6) = 27.10075251, (4, 7) = 40.26736031, (4, 8) = 57.11215315, (5, 1) = 1., (5, 2) = -7.181375466, (5, 3) = 6.777193107, (5, 4) = 12.19170970, (5, 5) = 9.600555508, (5, 6) = 7.084730200, (5, 7) = 11.13249218, (5, 8) = 24.60731420, (6, 1) = 1., (6, 2) = -10.92878792, (6, 3) = 28.28352183, (6, 4) = -10.19173665, (6, 5) = -20.04576479, (6, 6) = 9.17677094, (6, 7) = 39.97816692, (6, 8) = 49.07345342, (7, 1) = 1., (7, 2) = -16.09078867, (7, 3) = 78.08969329, (7, 4) = -166.5158779, (7, 5) = 129.0586058, (7, 6) = 104.8307190, (7, 7) = -104.838425, (7, 8) = -111.0119440, (8, 1) = 1., (8, 2) = -23.55908364, (8, 3) = 192.6052140, (8, 4) = -856.8131732, (8, 5) = 2255.610395, (8, 6) = -3256.154493, (8, 7) = 1577.05254, (8, 8) = 2063.443568})

(5)

NULL

# ------------------------------------------------- --------------------------
# 2 / حساب مصفوفة (ب) من قبل أدومين بوليس لمصطلح غير الخطية.

"G(y):=(e)^(y)"

proc (y) options operator, arrow; exp(y) end proc

(6)

"g(x):=evalf(((4*sqrt(x))/(sqrt(Pi)))+(8/(3))*((x^(3/(2)))/(sqrt(Pi)))+2*x+x^(2)+(e)^(x^(2)))"

proc (x) options operator, arrow; evalf(4*sqrt(x)/sqrt(Pi)+(8/3)*x^(3/2)/sqrt(Pi)+2*x+x^2+exp(x^2)) end proc

(7)

#Find أدومين بولي:

for k from 0 to n-1 do AP[k] := evalf(subs(lambda = 0, (diff(G(sum(y[t]*lambda^t, t = 0 .. k)), [`$`(lambda, k)]))/factorial(k))) end do

exp(y[0])

 

y[1]*exp(y[0])

 

y[2]*exp(y[0])+.5000000000*y[1]^2*exp(y[0])

 

y[3]*exp(y[0])+y[2]*y[1]*exp(y[0])+.1666666667*y[1]^3*exp(y[0])

 

y[4]*exp(y[0])+y[3]*y[1]*exp(y[0])+.5000000000*y[2]^2*exp(y[0])+.5000000000*y[2]*y[1]^2*exp(y[0])+0.4166666667e-1*y[1]^4*exp(y[0])

 

y[5]*exp(y[0])+y[4]*y[1]*exp(y[0])+y[3]*y[2]*exp(y[0])+.5000000000*y[3]*y[1]^2*exp(y[0])+.5000000000*y[2]^2*y[1]*exp(y[0])+.1666666667*y[2]*y[1]^3*exp(y[0])+0.8333333333e-2*y[1]^5*exp(y[0])

 

y[6]*exp(y[0])+y[5]*y[1]*exp(y[0])+y[4]*y[2]*exp(y[0])+.5000000000*y[4]*y[1]^2*exp(y[0])+.5000000000*y[3]^2*exp(y[0])+y[3]*y[2]*y[1]*exp(y[0])+.1666666667*y[3]*y[1]^3*exp(y[0])+.1666666667*y[2]^3*exp(y[0])+.2500000000*y[2]^2*y[1]^2*exp(y[0])+0.4166666667e-1*y[2]*y[1]^4*exp(y[0])+0.1388888889e-2*y[1]^6*exp(y[0])

 

y[7]*exp(y[0])+.5000000000*y[3]*y[2]*y[1]^2*exp(y[0])+.5000000000*y[5]*y[1]^2*exp(y[0])+y[5]*y[2]*exp(y[0])+y[6]*y[1]*exp(y[0])+y[4]*y[3]*exp(y[0])+.5000000000*y[3]^2*y[1]*exp(y[0])+.1666666667*y[2]^3*y[1]*exp(y[0])+0.1984126984e-3*y[1]^7*exp(y[0])+y[4]*y[2]*y[1]*exp(y[0])+0.8333333333e-2*y[2]*y[1]^5*exp(y[0])+0.8333333333e-1*y[2]^2*y[1]^3*exp(y[0])+0.4166666667e-1*y[3]*y[1]^4*exp(y[0])+.5000000000*y[3]*y[2]^2*exp(y[0])+.1666666667*y[4]*y[1]^3*exp(y[0])

(8)

NULL

#Find a ماتريسز b ^ (k) و C ^ (k): = A ^ (- 1) * b ^ (k)، ثم ايجاد حل تقريبي Y [k]: = سوم (C ^ (k) [i ] * L [i]، i = 1 .. n ):

# 1) البحث ب (0)

b0 := array(1 .. n, 1 .. m-7); for i to 2 do b0[i, 1] := 0 end do; for i from 3 to n do b0[i, 1] := evalf(subs(x = x[i], g(x[i]))) end do

print(`b0=`, b0)

`b0=`, b0

(9)

b0 := convert(b0, Matrix)

b0 := Matrix(8, 1, {(1, 1) = 0, (2, 1) = 0, (3, 1) = 5.533921684, (4, 1) = 10.78339161, (5, 1) = 69.22208674, (6, 1) = 96372.14332, (7, 1) = 0.5649990671e13, (8, 1) = 0.2063418920e32})

(10)

# 2) البحث عن ج (0)

C0 := LinearSolve(A, b0)

C0 := Matrix(8, 1, {(1, 1) = -0.11474558283495975e27, (2, 1) = -0.6041534517526968e26, (3, 1) = 0.28431046341368933e27, (4, 1) = -0.1109483456679843e28, (5, 1) = 0.2601411410469915e28, (6, 1) = -0.34736953613415415e28, (7, 1) = 0.23829217145639085e28, (8, 1) = -0.634449734180237e27}, datatype = float[8])

(11)

for i to n do k0[i] := C0[i, 1] end do

HFloat(-1.1474558283495975e26)

 

HFloat(-6.041534517526968e25)

 

HFloat(2.8431046341368933e26)

 

HFloat(-1.109483456679843e27)

 

HFloat(2.601411410469915e27)

 

HFloat(-3.4736953613415415e27)

 

HFloat(2.3829217145639085e27)

 

HFloat(-6.34449734180237e26)

(12)

# 3) البحث عن y (0)

y[0] := sum(k0[s]*L(s-1, 2*x-1), s = 1 .. 8)

-HFloat (5.083969685801073e25) -HFloat (1.4661238981264424e26) * س + HFloat (1.2387812172594187e26) * (2 * س 1) ^ 2-HFloat (1.9836944590452831e24) * (2 * س 1) ^ 3 HFloat (5.120751558697758 E25) * (2 * س 1) ^ 4 + HFloat (2.0830079097858884e25) * (2 * س 1) ^ 5 HFloat (2.8586478120802086e24) * (2 * س 1) ^ 6 + HFloat (1.2588288376592004e23) * (2 * س 1) ^ 7

(13)

# -------------------------

#Find b (1)

لا شيء

لا شيء

لا شيء

b1: = أري (1 .. n، 1 .. m-7)؛  ل i تو 2 دو b1 [i، 1]: = 0 إند دو؛  من i إلى n n b1 [i، 1]: = سوبس (x = x [i]، أب [0]) إند دو

برينت (`b1 =`، b1)

`b1 =`، b1

(14)

b1: = كونفيرت (b1، ماتريكس)

b1: = مصفوفة (8، 1، {(1، 1) = 0، (2، 1) = 0، (3، 1) = إكس (هفلوات (-1.3446720400287247e26))، (4، 1) = إكس هفلوت (-1.000132892371102e26))، (5، 1) = إكس (هفلوت (-1.7743764624635952e26))، (6، 1) = إكس (هفلوت (9.701444095568667e26))، (7، 1) = إكس 1.9741498268709318e28))، (8، 1) = إكس (هفلوات (4.2920269682087554e30))})

(15)

لا شيء

# 2) البحث ج (1)

لينيرزولف (A، b1)

المصفوفة ([هفلوات (هفلوات (وندفيند))]، [هفلوت (هفلوات (وندفيند))]، [هفلوات (هفلوات (وندفيند))]، [هفلوات (هفلوات (وندفيند))]، [هفلوات (هفلوات (وندفيند) )، [هفلوات (هفلوات (وندفيند))]، [هفلوات (هفلوات (وندفيند))]، [هفلوات (هفلوات (وندفيند))]])

(16)

لا شيء


 

تحميل jam.mw

Hi everybody,

I want to solve numerically an ode and I get this error (undocumented on the maplesoft web site https://www.maplesoft.com/support/help/errors/....)

Error, (in sol) maximum number of event iterations reached (100) at t=2.6610663

I understand where this error can come from but the help pages don't say anything to fix this.
There is some stuff about round-off that could help but I don't understand how to use it.

I would be grateful if you provide me some help.
Thanks in advance


Download ErrorWithDsolve.mw

 

 

Dear 

Hope everyone is fine. In attached file I solved system of equations. But the solution like this 

Sol[1]:={{...},{...}}

But I want the solution like

Sol[1]:={...}

Please see the attachment and fix my problem

Problem.mw

Dear

I am facing to eliminate diff(p(x, y), y, x) from Eq1 and Eq2. My procedure is given below:

Eq1 := 2*rho[nf]*a^2*x*(diff(f(eta), eta, eta))*(diff(f(eta), eta))/h+rho[nf]*sqrt(nu[f])*(diff(f(eta), eta))*a*x*(diff(f(eta), eta, eta))/h^2+rho[nf]*sqrt(nu[f])*f(eta)*a*x*(diff(f(eta), eta, eta, eta))/h^2+2*rho[nf]*omega[0]*a*x*(diff(g(eta), eta))/h = -(diff(p(x, y), y, x))+mu[nf]*a*x*(diff(f(eta), eta, eta, eta, eta))/h^3-sigma[nf]*B[0]^2*a*x*(diff(f(eta), eta, eta))/h;

Eq2 := 0 = -(diff(p(x, y), y, x));

eliminate({Eq1, Eq2}, diff(p(x, y), y, x));

Dear 

I want to graw following points (u[i,j], i=0..M,j=0..N) obtained in Sol[i] in 3D where i takes along x-axes, j y-axis and u along z axes. I also want the style of point plot as surface. Same do for v and w. I am waiting your response, Thanks

3D_plots.mw

Dear

I want to draw the graphs of the attached system of PDEs for different values of M in 3D please fix my problem. I am waiting your positive response.

graphs_for_pde.mw

Dearz 

I want to ask how to run multiple program at a time in maple? I am waiting your positive response. 

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