Maple 15 Questions and Posts

These are Posts and Questions associated with the product, Maple 15

Hello everybody,

While i was trying to work on a physical math problem, a system of 4 integral equations is obtained. The right hand sides of these equations are known functions of r. The left hand sides contain double integrals with respect to lambda and t. i believe that an analytical determination of the 4 unknown functions f_1(t), f_2(t), f_3(t), and f_4(t) is far from being trivial, thus recourse to a numerical technique is necessary and indispensable.

 

i tried to express the unknown functions as series expansions in t and solve the resulting linear system of equations for the expansion coefficients, but unfortunately the coefficients are very large and the solution is strongly dependent on the number of coefficients. i was wondering whether someone here has some experience with such integral problems and is willing to assist and help. Any hint is highly appreciated.

 

i attach a Maple script including the equations.

Thank you,

 

>>>>>> Question.mw

what is the wrong in this operations for isentropic process ( isentropic-process) 

 

Restart: with(RealDomain) : interface(dispalyprecision=4) : ; Isentropical := proc(N,v) local K,PTR,KM1,KP1,GO, M,MS,C,PPT,TTT,RRT,AAS,eq,o ; K : = G() : KM1 : = k - 1 : KP1 : = K + 1 : GO := 1 : If N=1 then M := v Elif N=2 then PPT := v : M := sqrt ( 2 * (PPT^(-KM/K) -1 ) : Elif N=3 then MS := v : M := sqrt ( 1 / (KP1/ (2*MS^2) –KM1/2 ) : Elif N=4 then C := v : M := sqrt ( 2 / (KM1* (1 /(C^2) -1 )) ) : Elif N=5 then TTT := v : M := sqrt ( 2 * (1/TTT-1 ) / KM1 : Elif N=6 then RRT := v : M := sqrt ( 2 * (1/RRT^KM1 -1 ) / KM1 : Elif N=7 then AAS := v : eq :=AAS- (2*(1+KM1*M^2/2)/ KP1) ^ (KP1/ (2*KM1)) /M : M := fsolve(eq,M,0..1) : GO :=2 : Elif N=8 then AAS := v : eq :=AAS- (2*(1+KM1*M^2/2)/ KP1) ^ (KP1/ (2*KM1)) /M : M := fsolve(eq,M,1..infinity) : GO :=2 : Fi:fi GO<>2 then ASS := (2 *(1+ KM1*M^2/2/KP1) ^ (KP1/ (2*KM1)) /M fi: PTR := (1+ KM1*M^2/2/KP1) : PPT := PTR^(-K/KM1) : TTT:=PTR^ (-1) : RRT:+PTR^(-1/KM1) : If N <> 3 then MS := sqrt ( KP1 / ( 2 / ( M^2)+KM1) ) If N <> 3 then C := sqrt( 1 / (2 / (KM1*M^2) + 1 ) ) O := evalf([m,1./PPT,MS,C,1./TTT,1./RRT,AAS]) end : irp := proc (N, v) local f; f:=Isentropic1(N,v) : printf(cat(`% 9.4f `$7, ` \ n`) , f[ii$ii=1..7]) end : G := ( ) -> 1.4 : For mi form .1 to .5 do irp(1.mi) od : > > > Eq := table( [ (M2) = M2 , (MS2) = (K+1) /2 (2 / ( M2)+ (K-1) ) (C2) = 1 / (2 / (K-1)*M2+1 ) (PP0) = (1+(K-1)*M2/2)^(-K/(K-1) ) (RR0) = (1+(K-1)*M2/2)^(-1/(K-1) ) (TT0) = (1+(K-1)*M2/2)^(-1) (AAS) = (2 *(1 +(K-1)*M2/2 ) / (K+1) )^( (k-1) /(2*(k-1)))/ squt(M2) ]) : if vL=M then M2v := solve ( M2 -Eq[M2 ] , M2 ) : M2v := eval(M2v ,M2 = VR^2 ) : elif vL=MS then M2v := solve( M2 -Eq[MS2 ] , M2 ) : M2v := eval(M2v ,MS2 = VR^2 ) : elif vL=C then M2v := solve( M2 -Eq[C2 ] , M2 ) : M2v := eval(M2v ,C2 = VR^2 ) : elif vL=PP0 then M2v := solve( M2 -Eq[PP0] , M2 ) : M2v := eval(M2v ,PP0 = VR ) : elif vL=RR0 then M2v := solve( M2 -Eq[RR0] , M2 ) : M2v := eval(M2v ,RR0 = VR ) : elif vL=TT0 then M2v := solve( M2 -Eq[TT0] , M2 ) : M2v := eval(M2v ,TT0 = VR ) : elif vL=AASsub then M2v := fsolve( M2 -Eq[AAS] , M2 ) : M2 :=0..1 : elif vL=AASup then M2v := fsolve( M2 -Eq[AAS] , M2 ) : M2 :=1..infinity : fi: Eqsva1 := eva1(Eq, M2 = M2v) : Eqava1 [M] := sqrt(EqsVa1[M2] ) : Eqsva1[MS] := sqrt(EqsVa1[MS2] ) : Eqava1 [C] := sqrt(EqsVa1[C2] ) : 1var := [M, MS, C, PP0, RR0, TT0, AAS] : [seq(1var[i]=EqsVA1[1var[i] ] , I=1…nope(1var))] end: Egs :=[M=0.5, MS=0.53452, C=0.2182, P0P=0.84302, RR0=0.88517, TT0=0.95238, AASsub=1.33985, AASsup=0.95238] : For i from 1 to nops(Egs) do print(I,Isentropic2(Egs[i])) od : (process)

Suppose that A is an nxn matrix over the finite field Z:=GF(2,q) for some q. I wan to get the smitform of A over Z. First I used the package  

with(LinearAlgebra[Generic]) 

and after that I applied the command 

S := SmithForm[Z](A)

but the mentioned command made some errors. In fact, I do not how to define commands igcdex, iquo, irem, sign and abs for SmithForm over finite fields.

Thanks for any suggestions 

Hi. Can anyone help me with this error, it says 

Error, (in unknown) cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

 

restart

Shootlib := "F:\MAPLE\3";

"F:MAPLE3"

(1)

libname := Shootlib, libname;

"F:MAPLE3", "C:\Program Files\Maple 2015\lib", "."

(2)

with(Shoot);

[shoot]

(3)

with(plots):

``

FNS := {`&phi;p`(eta), f(eta), fp(eta), fpp(eta), fppp(eta), phi(eta), theta(eta), `&theta;p`(eta)}

{`&phi;p`(eta), f(eta), fp(eta), fpp(eta), fppp(eta), phi(eta), theta(eta), `&theta;p`(eta)}

(4)

ODE := {diff(`&phi;p`(eta), eta) = (-f(eta)*`&phi;p`(eta)+K*phi(eta)*(1-phi(eta))^2)*Sc, diff(f(eta), eta) = fp(eta), diff(fp(eta), eta) = fpp(eta), diff(fpp(eta), eta) = fppp(eta), diff(fppp(eta), eta) = (-fppp(eta)-f(eta)*fpp(eta)+k1*(2*fp(eta)*fppp(eta)-fpp(eta)^2)+lambda*fp(eta)+(1+Fr)*fp(eta)^2)/(k1*f(eta)), diff(phi(eta), eta) = `&phi;p`(eta), diff(theta(eta), eta) = `&theta;p`(eta), diff(`&theta;p`(eta), eta) = (-f(eta)*`&theta;p`(eta)+y*f(eta)*fp(eta)*`&theta;p`(eta))/(1/Pr-y*f(eta)^2)}

{diff(`&phi;p`(eta), eta) = (-f(eta)*`&phi;p`(eta)+K*phi(eta)*(1-phi(eta))^2)*Sc, diff(f(eta), eta) = fp(eta), diff(fp(eta), eta) = fpp(eta), diff(fpp(eta), eta) = fppp(eta), diff(fppp(eta), eta) = (-fppp(eta)-f(eta)*fpp(eta)+k1*(2*fp(eta)*fppp(eta)-fpp(eta)^2)+lambda*fp(eta)+(1+Fr)*fp(eta)^2)/(k1*f(eta)), diff(phi(eta), eta) = `&phi;p`(eta), diff(theta(eta), eta) = `&theta;p`(eta), diff(`&theta;p`(eta), eta) = (-f(eta)*`&theta;p`(eta)+y*f(eta)*fp(eta)*`&theta;p`(eta))/(1/Pr-y*f(eta)^2)}

(5)

blt := 4.; 1; IC := {`&phi;p`(0) = Psi, f(0) = 0, fp(0) = 1, fpp(0) = 0, fppp(0) = alpha, phi(0) = 0, theta(0) = 1, `&theta;p`(0) = beta}

4.

 

{`&phi;p`(0) = Psi, f(0) = 0, fp(0) = 1, fpp(0) = 0, fppp(0) = alpha, phi(0) = 0, theta(0) = 1, `&theta;p`(0) = beta}

(6)

BC := {fp(blt) = 0, fpp(blt) = 0, phi(blt) = 1, theta(blt) = 0};

{fp(4.) = 0, fpp(4.) = 0, phi(4.) = 1, theta(4.) = 0}

(7)

``

infolevel[Shoot:-shoot] := 1:

.7

 

1.0

 

.2

 

.2

 

1.0

 

.3

 

.5

 

.3

(8)

S := shoot(ODE, IC, BC, FNS, [alpha = 3.0125, beta = -2.31, Psi = -0.])

shoot: Step #  1

shoot: Parameter values :  alpha = 3.0125 beta = -2.31 Psi = -0.

Error, (in unknown) cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

 

p := odeplot(S, [eta, fp(eta)], 0 .. 15)

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

display(p)

Error, (in plots:-display) expecting plot structure but received: p

 

p2 := odeplot(S, [eta, theta(eta)], 0 .. 10)

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

display(p2)

Error, (in plots:-display) expecting plot structure but received: p2

 

p3 := odeplot(S, [eta, phi(eta)], 0 .. 10)

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

display(p3)

Error, (in plots:-display) expecting plot structure but received: p3

 


 

Download Darcy.mw

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

what package I need to add in order to use commands named "Drawmatrix, Translatemat and Transform" ? I add package named Lamp but it is not working. I have maple 15. Please try to respond as soon as possible because its urgent.

 

Thank you

Dear all

Hope everything is fine with everything. I want to draw the graph of the u(x,0.5) and T(x,0.5) for different values of alpha like alpha =0.4,0.6,0.8 while keeping Gr, R and Pr are fixed. Please solve the following problem I shall be vary thankful to you. Thanks in advance

with the following BCs

Dears 

Hope you would be fine. I want to solve the following PDEs by numerically for v[nf]=alpha[nf]=Ec=mu[nf]=C=1 and Pr=6.2

Eq1 := diff(u(x, t), t) = v[nf]*(diff(u(x, t), x, x));

Eq2 := diff(u(x, t), t) = alpha[nf]*(diff(theta(x, t), x, x))/Pr+Ec*mu[nf]*C*(diff(u(x, t), x))^2;

ICs := u(x, 0) = 0, theta(x, 0);

BCs := u(0, t) = 1, theta(0, t) = 1, u(10, t) = 0, theta(10, t) = 0;

and find the values of (diff(u(0, t), x))/(1-phi)^2.5 for different values of phi. Thanks in advace 

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

Hello

Hope everything going fine with you. I am facing problem to fine the exact (numerical) solution of the attached system of linear PDEs associated with BSc and ICs. I tried to solve it without BCs and ICs, with BCs and with ICs also all the times I failed. Please solve it either general, with ICs or BCs. You can try to solve it numrically. In attached file H(t) represent the unit step function. I am waiting your positive response.

PDEs_solve.mw 

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

What shall I do to install Maple 15 and MapleSym 5 in a Windos 10 environment.

I find the procedure in Maplesoft site up to Windows 8.

May I follow it for Windows 10.

Thank you for any help. Kind regards

Im trying to solve 12 equations with 12 variables but I can't solve. Please help and advise me to solve this problem. Iproject3.mw
project3.mw

 

 

 

Dear All

I calculate something with gr tensor, for example Ricciscalar. How can I save it in maple memory? As you know, in this situation you can not use your calculation directly and it seems that it saved in grtensor memory not maple memory. For example, if you want to plot Ricciscalar, you should save it as a new definition in maple and then plot it. 

Thank you.

how we can solve an ode with boundaries by using RK4 and any other technique??

how we can solve an ode with exat soltuion n calculate the unknw constant which aries after solving an ode.???

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