Questions - MaplePrimes

How do I use Homotopy Perturbation Method to find ...

Asked by: kennywhyte 0

May 23 2019

0 0

Please, I need to use Maple to solve Euler-Bernoulli Beam on Pasternak Foundation using Homotopy Perturbation Method.

The governing equation is

initial conditions are

the boundary condition is

The governing equation represents Euler-Bernoulli beam on a generalized Pasternak viscoelastic foundation under an
arbitrary distributed dynamic load. in which E, I , ρ ,A are the parameters of the beam, representing Young’s modulus of elasticity, moment of inertia, density and area of cross section, respectively. K,C and Gp are spring stiffness, damping coefficient, and shear coefficient of the foundation. Moreover, y(x, t) and F(x, t) are defined as the vertical deflection of the beam and the generic arbitrary dynamic loads, respectively, where the loads distribute along the x-axis and t is time.

I will appreciate anyone who can help me with a Maple solution.

Thank you.

Inconsistently working if-statements within a proc...

Asked by: abecke12 10

May 23 2019

2 21

Would anybody be able to explain to me why I had to rewrite this one baby-procedure that has an if-statement inside my larger procedure, so that I could get a later on if-statement to work? As best I can tell, they mean exactly the same thing.

Information that may be pertinent:

- The entire (overall) procedure worked without throwing any warnings prior to my adding this new if-statement.
- The if-statement itself worked perfectly fine on another worksheet, though I hadn't tested it inside a procedure.
- Commenting out the if-statement but retaining the interior commands led to the sheet compiling again, showing that it was in fact the presence of the if-statement causing the issue.
- When I commented out the offending baby-procedure that started throwing the warning, the sheet once again compiled.

The added if statement:

if eval_size > 4 then Search(max(seq(eval_cont[i], i = 4 .. eval_size)), eval_cont); evals_pairlist := evals_pairlist[[1 .. 3, %]] fi:

The error I get, and its "positioning":

Error, invalid expression for inline function

remove some errors...

Asked by: torabi 90

May 23 2019

0 16

Hello,

How I can remove some problems in my code.

I wrote it before in software, but in some lines, I have some problems with it.

How I can change it in maple to run well?

>

M := 2; B := 1; C := 3; K := 6; f := 2*exp(-t); q0 := 1; qd0 := -1; qd20 := 1; alpha := 1/2; beta := 1/12; gammaa := 1/4; h := .1; Tf := 2

>	$"N:=size(M,1) T:=0:h:Tf; lt:=length(T); F:=subs(f,t,T); F:=subs(t=T,f); qd30:=M\(F(1)-Bqd20-Cqd0-K*q0); q:=zeros(N,lt) qd:=zeros(N,lt) qd2:=zeros(N,lt); qd3:=zeros(N,lt); q(:,1):=q0 qd(:,1):=qd0 qd2(:,1):=qd20 qd3(:,1):=qd30"$

Error, invalid function arguments

$"N:=size(M,1) T:=0:h:Tf; lt:=length(T); F:=subs(f,t,T); F:=subs(t=T,f); qd30:=M\(F(1)-B*qd20-C*qd0-K*q0); q:=zeros(N,lt) qd:=zeros(N,lt) qd2:=zeros(N,lt); qd3:=zeros(N,lt); q(:,1):=q0 qd(:,1):=qd0 qd2(:,1):=qd20 qd3(:,1):=qd30"$

>

$"A:=M+alpha*h*B+gammaa*(h^2)*C+beta*(h^3)*K; for n:=1:lt-1 do D:=F(n+1)-B*(qd2(:,n)+(1-alpha)*h*qd3(:,n))-... C*(qd(:,n)+h*qd2(:,n)+(0.5-gammaa)*(h^2)*qd3(:,n))-... K*(q(:,n)+h*qd(:,n)+(h^2)/2*qd2(:,n)+(1/6-beta)*(h^3)*qd3(:,n)); qd3(:,n+1):=A\D; qd2(:,n+1):=qd2(:,n)+(1-alpha)*h*qd3(:,n)+alpha*h*qd3(:,n+1); qd(:,n+1):=qd(:,n)+h*qd2(:,n)+(0.5-gammaa)*(h^2)*qd3(:,n)+gammaa*(h^2)*qd3(:,n+1); q(:,n+1):=q(:,n)+h*qd(:,n)+(h^2)/2*qd2(:,n)+(1/6-beta)*(h^3)*qd3(:,n)+... beta*(h^3)*qd3(:,n+1); end do"$

Error, invalid function arguments

$"A:=M+alpha*h*B+gammaa*(h^2)*C+beta*(h^3)*K; for n:=1:lt-1 do D:=F(n+1)-B*(qd2(:,n)+(1-alpha)*h*qd3(:,n))-... C*(qd(:,n)+h*qd2(:,n)+(0.5-gammaa)*(h^2)*qd3(:,n))-... K*(q(:,n)+h*qd(:,n)+(h^2)/2*qd2(:,n)+(1/6-beta)*(h^3)*qd3(:,n)); qd3(:,n+1):=A\D; qd2(:,n+1):=qd2(:,n)+(1-alpha)*h*qd3(:,n)+alpha*h*qd3(:,n+1); qd(:,n+1):=qd(:,n)+h*qd2(:,n)+(0.5-gammaa)*(h^2)*qd3(:,n)+gammaa*(h^2)*qd3(:,n+1); q(:,n+1):=q(:,n)+h*qd(:,n)+(h^2)/2*qd2(:,n)+(1/6-beta)*(h^3)*qd3(:,n)+... beta*(h^3)*qd3(:,n+1); end do"$

>

Error, (in plot) unexpected options: [r-o, , 1.5]

>

Download

write whlie loop ...

Asked by: reza gugheri 20

May 23 2019

0 2

How should wirte a while loop for solve nonlinear equations by newton raphson method

homotopy pertubation...

Asked by: Gabriel samaila 35

May 23 2019

0 4

Hi guys,
I am trying write a code for homotopy perturbation, i have already generated the polynomial as you can see, i have also solve for concentration equation since is not couple. But i have a lot of error massages for temperature, velocity and induced magnetic field. can some one please go through the code?

>

>	PDEtools[declare](f(x),theta(x),u(x),w(x), prime=x):

(1)

>

>	f(x):=sum((p^(i))*f[i](x),i=0..N);

(2)

>

(3)

>

(4)

>

(5)

>

(6)

>

HPMEr := (1-p)*(diff(theta(x), `$`(x, 2)))+p*(diff(theta(x), `$`(x, 2))-k11*(diff(theta(x), x))+k12*(diff(u(x), x))^2+k13*(diff(w(x), x))^2+k14*theta(x));

(7)

>

(8)

>

(9)

>

(10)

>

diff(diff(theta[3](x), x), x)+k12*(2*(diff(u[0](x), x))*(diff(u[2](x), x))+(diff(u[1](x), x))^2)+k14*theta[2](x)+k13*(2*(diff(w[0](x), x))*(diff(w[2](x), x))+(diff(w[1](x), x))^2)-k11*(diff(theta[2](x), x)) = 0

diff(diff(theta[4](x), x), x)+k12*(2*(diff(u[0](x), x))*(diff(u[3](x), x))+2*(diff(u[1](x), x))*(diff(u[2](x), x)))-k11*(diff(theta[3](x), x))+k14*theta[3](x)+k13*(2*(diff(w[0](x), x))*(diff(w[3](x), x))+2*(diff(w[1](x), x))*(diff(w[2](x), x))) = 0

(11)

>

(12)

>

(13)

>

con[1][0] := f[0](-1) = 1, f[0](1) = 1:

2.400000000*k2+0.3589208394e-1*k2^4+1.104000000*k2^2+2.713333334*k1*k2+1.904000000*k1^2*k2+0.115520003e-1*k2^3+.939244445*k1*k2^2+.3973226666*k1^2*k2^2+0.1412642116e-1*k1*k2^3+.9218444444*k1^3*k2

(14)

>

"cond[1][0]:=theta[0](-1)=0.1, theta[0](1)=1,w[0](-1)=0, w[0](1)=0,u[0](-1)=0, u[0](1)=0: for j from 1 to N do: cond[1][j]:=theta[j](-1)=0, theta[j](1)=0,w[j](-1)=0, w[j](1)=0,u[j](-1)=0, u[j](1)=0: end do: for i from 0 to N do: dsolve({equa[1][i],cond[1][i]},theta[i](x)); theta[i](x):=rhs(`%`): end do: theta(x):=evalf(simplify(sum(theta[n](x),n=0..N))); convert(theta(x),'rational'); "

Error, (in dsolve) found the following equations not depending on the unknowns of the input system: {u[0](-1) = 0, u[0](1) = 0, w[0](-1) = 0, w[0](1) = 0}

(15)

>

"condi[1][0]:=theta[0](-1)=0.1, theta[0](1)=1,w[0](-1)=0, w[0](1)=0,u[0](-1)=0, u[0](1)=0,f[0](-1)=1, f[0](1)=1: for j from 1 to N do: condi[1][j]:=theta[j](-1)=0, theta[j](1)=0,w[j](-1)=0, w[j](1)=0,u[j](-1)=0, u[j](1)=0, f[j](-1)=0, f[j](1)=0: end do: for i from 0 to N do: dsolve({equat[1][i],condi[1][i]},u[i](x)); u[i](x):=rhs(`%`): end do: u(x):=evalf(simplify(sum(u[n](x),n=0..N)))"

Error, (in dsolve) found the following equations not depending on the unknowns of the input system: {f[0](-1) = 1, f[0](1) = 1, w[0](-1) = 0, w[0](1) = 0, theta[0](-1) = 1/10, theta[0](1) = 1}

(16)

>

"condit[1][0]:=theta[0](-1)=0.1, theta[0](1)=1,w[0](-1)=0, w[0](1)=0,u[0](-1)=0, u[0](1)=0,f[0](-1)=1, f[0](1)=1: for j from 1 to N do: condit[1][j]:=theta[j](-1)=0, theta[j](1)=0,w[j](-1)=0, w[j](1)=0,u[j](-1)=0, u[j](1)=0, f[j](-1)=0, f[j](1)=0: end do: for i from 0 to N do: dsolve({equati[1][i],condit[1][i]},w[i](x)); w[i](x):=rhs(`%`): end do: w(x):=evalf(simplify(sum(w[n](x),n=0..N)))"

Error, (in dsolve) found the following equations not depending on the unknowns of the input system: {f[0](-1) = 1, f[0](1) = 1, u[0](-1) = 0, u[0](1) = 0, theta[0](-1) = 1/10, theta[0](1) = 1}

(17)

>

Download completecode.mw

Problem with system of equation?...

Asked by: nedradan 10

May 23 2019

1 3

Hello,

I got some problems with command solve .

I have to solve 6 equations with 6 unknowns. The problem is that Maple solves this system in a wrong way - the values calculated by the command are bad. I would like to ask if there is any command in Maple while solving the equations that are responsible for possible approximations when solving equations.
In the attachment I will insert the code I used.

https://www.pastiebin.com/5ce6a1943f548

How can i solve "which is not valid for its 2nd ar...

Asked by: shayas75 5

May 22 2019

1 5

Hi freind,

Anybody knows what happen to this coding?

why this error happens? how can i fix it?

thank you!

Edge thickness of arcs in DrawGraph...

Asked by: rstellian 45

May 22 2019

2 6

Hi everyone,

I was wondering how I could modify the thickness of edges in a graph displayed as a Maple plot through DrawGraph. The point is, the graph comprises 100 vertices and 1000 edges. By default, edge thickness is set as 2 but due to the high number of edges I would like to set edge thickness to1 or even 0. How can I do so?

Here is an example with a random graph:

with(GraphTheory) : with(RandomGraphs) : G := RandomGraph(100, 1000) : DrawGraph(G)

Thank you very much

Bug When Using IntegrationTools[Change] With Assum...

Asked by: TheAkashain 25

May 22 2019

2 2

Good day,

I was recently using Maple 2019 for work on a project, and ran into an error. This error (which will be copied and pasted below for others to test) occurs when making assumptions across multiple lines (whether using the additionally function or not) while using IntegrationTools[Change]. It seems that, if during the process a variable that was within both the assumptions is subtracted from itself, the subtraction fails to happen and leaves what effectively equals 0 in the workings, making further workings impossible.

I'm wondering if anyone else is able to reproduce this error? I know the fix for it is to not disjoint the assumptions, but I am curious if others can easily reproduce it or if others have experiences with it!

As promised, below you will find my workings in order to reproduce this error!

Base Error:

restart;
assume(a>0,b>0,b>a,c>0,t>0);
interface(showassumed=0);
F := Int(sqrt(d-a*c^2*t),d=0...infinity);
assume(b>a);
IntegrationTools[Change](F,-a*t*c^2+d=-y,y)

Simple Fix:

restart;
assume(a>0,b>0,b>a,c>0,t>0);
interface(showassumed=0);
F := Int(sqrt(d-a*c^2*t),d=0...infinity);
IntegrationTools[Change](F,-a*t*c^2+d=-y,y)

Error Without Interface Change:

restart;
assume(a>0,b>a,c>0,t>0);
F := Int(sqrt(d-a*c^2*t),d=0...infinity);
assume(b>a);
IntegrationTools[Change](F,-a*t*c^2+d=-y,y)

Error When Using Additionally:

restart;
assume(a>0,b>a,c>0,t>0);
interface(showassumed=0);
F := Int(sqrt(d-a*c^2*t),d=0...infinity);
additionally(b>a);
IntegrationTools[Change](F,-a*t*c^2+d=-y,y)

fix simplify problem...

Asked by: bashar27 55

May 22 2019

0 2

restart;
lambda := 1;
1
mu := 1;
1
alpha := 1;
1
v := 2;
2
delta := 1;
1
m := 1;
1
d := 3;
3
l := 1;
1
omega := -(1/2)*a*lambda^2-a*m^2+2*a*mu*v-delta*l*m-(1/2)*delta*lambda^2+2*delta*mu*v-l^2*mu-(1/2)*lambda^2*mu+2*mu^2*v-2*a*mu-2*delta*mu-2*mu^2;
1
- a + 1
2
a[0] := ((2*d*v-2*d-lambda)*(1/2))*sqrt(2)*sqrt(gamma*(a+delta+mu))/gamma;
(1/2) (1/2)
5 2 (gamma (a + 2))
-----------------------------
2 gamma
a[1] := 0;
0
a[2] := -(2*(1/2))*sqrt(2)*sqrt(gamma*(a+delta+mu))*(d^2*v-d^2-d*lambda+mu)/gamma;
(1/2) (1/2)
7 2 (gamma (a + 2))
- -----------------------------
gamma
Omega := lambda^2-4*mu*v+4*mu;
-3
H := (-lambda+sqrt(-Omega)*tan((1/2)*sqrt(-Omega)*xi))/(2*(v-1));
1 1 (1/2) /1 (1/2) \
- - + - 3 tan|- 3 xi|
2 2 \2 /
u := a[0]+a[1]*(d+H)+a[2]/(d+H);
(1/2) (1/2)
5 2 (gamma (a + 2))
-----------------------------
2 gamma

(1/2) (1/2)
7 2 (gamma (a + 2))
- -------------------------------------
/5 1 (1/2) /1 (1/2) \\
gamma |- + - 3 tan|- 3 xi||
\2 2 \2 //

eta := -l*y-m*x+omega*t;
/1 \
-y - x + |- a + 1| t
\2 /
u := a[0]+a[1]*(d+H)+a[2]/(d+H);
(1/2) (1/2)
5 2 (gamma (a + 2))
-----------------------------
2 gamma

(1/2) (1/2)
7 2 (gamma (a + 2))
- -------------------------------------
/5 1 (1/2) /1 (1/2) \\
gamma |- + - 3 tan|- 3 xi||
\2 2 \2 //

f := diff(u, xi);
/ 2\
(1/2) (1/2) |3 3 /1 (1/2) \ |
7 2 (gamma (a + 2)) |- + - tan|- 3 xi| |
\4 4 \2 / /
-------------------------------------------------------
2
/5 1 (1/2) /1 (1/2) \\
gamma |- + - 3 tan|- 3 xi||
\2 2 \2 //
S := diff(u, xi);
/ 2\
(1/2) (1/2) |3 3 /1 (1/2) \ |
7 2 (gamma (a + 2)) |- + - tan|- 3 xi| |
\4 4 \2 / /
-------------------------------------------------------
2
/5 1 (1/2) /1 (1/2) \\
gamma |- + - 3 tan|- 3 xi||
\2 2 \2 //
xi := x+y-(-2*alpha*m-delta*l-delta*m-2*l*mu)*t;
x + y + 6 t
eq := (-omega-a*m*m-delta*l*m-mu*l*l)*u-(gamma*u*u)*u+(a+delta+mu)*S;
/ (1/2) (1/2)
/ 3 \ |5 2 (gamma (a + 2))
|- - a - 3| |-----------------------------
\ 2 / | 2 gamma
|
\

(1/2) (1/2) \ /
7 2 (gamma (a + 2)) | |
- ------------------------------------------------| - gamma |
/5 1 (1/2) /1 (1/2) \\| |
gamma |- + - 3 tan|- 3 (x + y + 6 t)||| |
\2 2 \2 /// \

(1/2) (1/2)
5 2 (gamma (a + 2))
-----------------------------
2 gamma

(1/2) (1/2) \
7 2 (gamma (a + 2)) |
- ------------------------------------------------|^3 +
/5 1 (1/2) /1 (1/2) \\|
gamma |- + - 3 tan|- 3 (x + y + 6 t)|||
\2 2 \2 ///

/
1 |
------------------------------------------------- |7 (a + 2)
2 \
/5 1 (1/2) /1 (1/2) \\
gamma |- + - 3 tan|- 3 (x + y + 6 t)||
\2 2 \2 //

/ 2
(1/2) (1/2) |3 3 /1 (1/2) \
2 (gamma (a + 2)) |- + - tan|- 3 (x + y + 6 t)|
\4 4 \2 /

\\
||
||
//
value(%);
/ (1/2) (1/2)
/ 3 \ |5 2 (gamma (a + 2))
|- - a - 3| |-----------------------------
\ 2 / | 2 gamma
|
\

(1/2) (1/2) \ /
7 2 (gamma (a + 2)) | |
- ------------------------------------------------| - gamma |
/5 1 (1/2) /1 (1/2) \\| |
gamma |- + - 3 tan|- 3 (x + y + 6 t)||| |
\2 2 \2 /// \

(1/2) (1/2)
5 2 (gamma (a + 2))
-----------------------------
2 gamma

(1/2) (1/2) \
7 2 (gamma (a + 2)) |
- ------------------------------------------------|^3 +
/5 1 (1/2) /1 (1/2) \\|
gamma |- + - 3 tan|- 3 (x + y + 6 t)|||
\2 2 \2 ///

/
1 |
------------------------------------------------- |7 (a + 2)
2 \
/5 1 (1/2) /1 (1/2) \\
gamma |- + - 3 tan|- 3 (x + y + 6 t)||
\2 2 \2 //

/ 2
(1/2) (1/2) |3 3 /1 (1/2) \
2 (gamma (a + 2)) |- + - tan|- 3 (x + y + 6 t)|
\4 4 \2 /

\\
||
||
//

simplify(%);
Error, (in simplify/tools/_zn) too many levels of recursion

fix the problem pls...

Asked by: bashar27 55

May 22 2019

0 1

Q := exp(I*(-y-x+((1/2)*a+1)*t))*((5/2)*sqrt(2)*sqrt(gamma*(a+2))/gamma-7*sqrt(2)*sqrt(gamma*(a+2))/(gamma*(5/2+(1/2)*sqrt(3)*tan((1/2)*sqrt(3)*(x+y+6*t)))));
/ (1/2) (1/2)
/ / /1 \ \\ |5 2 (gamma (a + 2))
exp|I |-y - x + |- a + 1| t|| |-----------------------------
\ \ \2 / // | 2 gamma
|
\

(1/2) (1/2) \
7 2 (gamma (a + 2)) |
- ------------------------------------------------|
/5 1 (1/2) /1 (1/2) \\|
gamma |- + - 3 tan|- 3 (x + y + 6 t)|||
\2 2 \2 ///
/ (1/2) (1/2)
/ / /1 \ \\ |5 2 (gamma (a + 2))
exp|I |-y - x + |- a + 1| t|| |-----------------------------
\ \ \2 / // | 2 gamma
|
\

(1/2) (1/2) \
7 2 (gamma (a + 2)) |
- ------------------------------------------------|
/5 1 (1/2) /1 (1/2) \\|
gamma |- + - 3 tan|- 3 (x + y + 6 t)|||
\2 2 \2 ///
plot3d(Re(Q), x = -40 .. -37, y = -40 .. -37, t = -10 .. 10);

how to use Maple to prove an equation based on a k...

Asked by: Janeasefor 35

May 22 2019

2 0

Dear Maple friends~

Recently I am thinking a question about how to use Maple to prove an equation based on a known partial differential equationand its boundary conditions.

Although I can Prove it with hand computation ,it still has some difficulty and it will be really hard if its partial differential equation become more complex(As a matter of fact, it will happen).So I think of Maple and want to take advantage of computer.However,I get few ideas how to realize it .The details are as follows：

alias(u=u(x,t)):
pde:=diff(u,t)-diff(u,x$2,t)+4*u^2*diff(u,x)=3*u*diff(u,x)*diff(u,x$2)+u^2*diff(u,x$3);
N:=5;#actually N can be any positive integer!
bcs:=eval(u,x=-infinity)=0,seq(eval(diff(u,x$ha),x=-infinity)=0,ha=1..N),eval(u,x=infinity)=0,seq(eval(diff(u,x$ha),x=infinity)=0,ha=1..N);
E:=Int(u^4+2*u^2*diff(u,x)^2-diff(u,x)^4/3,x=-infinity..infinity);

#try to prove the following equation
diff(E,t)=0

The written proof is as follows:

Therfore,I submit such a problem and look forward your solutions and suggestions sincerely~

How to not evaluate worksheet until i want...

Asked by: federicie 10

May 22 2019

2 3

Hy everyone,

i'm writing a code wich ends with an Explore including multiple parameters (8) ; my problem is that if i want to change every parameter, elaborating time becames too long, because Maple evaluates every variation of every parameter every time.
I'm looking for something like a button, which works like this: when i change parameters in explore maple doesn't evaluate the function, and when i click the button maple evaluates one time all the changed parameters.

Any suggestion?

Thanks in advance