Maple 13 Questions and Posts

These are Posts and Questions associated with the product, Maple 13

Hi everybody,

The Collatz conjecture can be used to give students a taste of a topic in Number Theory.  See the Wikipedia article for a good explaination.

https://en.wikipedia.org/wiki/Collatz_conjecture

Also, a conjecture is something that is probrably true.  Enjoy my little Maple procedure.  (in .mw and .pdf forms)

Collatz_third_time.mw

Collatz_third_time.pdf

Comments are appreciated.

Matt

 

HI MaplePrimes,

Is the Goldbach Weak Conjecture proven?

Consider odd primes p, q, and r.  The question is, Is the sum p+q+r sufficient to reach all odd numbers greater than 9?

See - 

https://en.wikipedia.org/wiki/Goldbach's_weak_conjecture

I tried an example.

looping_for_Goldbach_Weak_Conjecture_8.mw

looping_for_Goldbach_Weak_Conjecture_8.pdf

Regards,

Matt

 

My code :

> restart; with*PDEtools;

> PDE := diff(u(x, t), `$`(t, 2)) = 4*(diff(u(x, t), `$`(x, 2)));

> pdsolve({PDE, u(x, 0) = cos((1/2)*x), (D[1](u))(x, 0) = 0}, u(x, t));
 

And i get Error, (in pdsolve/BC) invalid input: indets expects 1 or 2 arguments, but received 3.Please help me find my Error.Thank you!!!

Hello, Sir 

I tried to execute the program for a set values for more than one parameter but it is not existing, please can you do a favor for me in this case, that is how to write a program to execute set of values for more than one parameter at a time and how to plot the graph?

 

stretching_cylinder_new.mw

 

HI MaplePrimes.com and other watchers,

Please enjoy the attaced files about combinatorics.
You may already know what '4 choose 3' is.

an_excercise_in_combinatorics.mw

an_excercise_in_combinatorics.pdf

Hopefully this can be useful to the casual mathematical observer.

Regards,

Matt

 

I am trying to plot f=[r^2 *cos(theta)+r*sin(theta)],as a DensityPlot[] in polar coordinates.

here r is a function of theta, r=r1(θ)..r2(θ) , for this reason, I have a problem to plot f in density plot

f=[r^2 *cos(theta)+r*sin(theta)];

r1(theta)= 0.3+0.1*cos(theta);
r2(theta)= 0.5+0.1*cos(theta);
display(changecoords(densityplot(f, r =r1(theta)..r2(theta), theta = 0 .. 2*Pi, style = patchnogrid, colorstyle = HUE), polar), axes = box, orientation = [270, 0], labels = [x, y, ``]);

(Error, (in plots/densityplot) bad range arguments r = .3+.1*cos(theta) .. .5+.1*cos(theta), theta = 0 .. 2*Pi )

Dear sir in this problem should accept five boundaryconditions but it is not working for five boundary conditions and showing the following error please can you tell why it is like this ??

Error, (in dsolve/numeric/bvp/convertsys) too many boundary conditions: expected 4, got 5
Error, (in plots:-display) expecting plot structures but received: [fplt[1], fplt[2], fplt[3], fplt[4], fplt[5], fplt[6], fplt[7]]
Error, (in plots:-display) expecting plot structures but received: [tplt[1], tplt[2], tplt[3], tplt[4], tplt[5], tplt[6], tplt[7]]
 

and for the progam please check the following link

stretching_cylinder_new1.mw

Hi MaplePrimes,

This YouTube video has a nice puzzle. 

It is titled "Can you solve the locker riddle". 
My first blush was to consider modular arithmatic
https://www.youtube.com/watch?v=c18GjbnZXMw

Here is a maple page -
divisors_excercise.mw

divisors_excercise.pdf

Have a very fine rest of the day.

Regards,
Matt

 

I assigned

before an algebraic calculation so I would like to get  or have the program print the 70 digits of the answer and not just 10 digits. Because when I press ENTER, I get only 10 digits.

 

Hi Maple Primes,

Can this code be improved?

I know that the Goldbach Conjecture has been checked with computer tools above 10^10.

Request for comments.

check_g_conjecture_26_b.mw

check_g_conjecture_26_b.pdf

Regards

Matt

 

staganation_point11.mw
 

``

restart

l := 1:

1

 

1.5

 

.5

 

[blue, green, red, yellow]

(1)

``

for j to nops(A) do R1 := 2*n/(n+1); R2 := 2*p/(n+1); R3 := 2/(n+1); sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R1*(1-(diff(f(eta), eta))^2)-M*(diff(f(eta), eta)) = 0, diff(diff(theta(eta), eta), eta)+pr*f(eta)*(diff(theta(eta), eta))-R2*pr*(diff(f(eta), eta))*theta(eta)+R3*(A[j]*(diff(f(eta), eta))+B*theta(eta)) = 0, f(0) = 1, (D(f))(0) = L+b*((D@@2)(f))(0), (D(f))(20) = 1, theta(0) = 1+s*(D(theta))(0), theta(20) = 0], numeric, method = bvp); plots[odeplot](sol1, [eta, ((D@@2)(f))(eta)], color = red); fplt[j] := plots[odeplot](sol1, [eta, diff(f(eta), eta)], color = K[j], axes = boxed); tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = K[j], axes = normal) end do:

 

 

``

l := 1:

1

 

[0, 1, 1.5]

 

.5

 

[blue, green, red, yellow]

(2)

for j to nops(n1) do R4 := 2*n1[j]/(n1[j]+1); R5 := 2*p1/(n1[j]+1); R6 := 2/(n1[j]+1); sol2 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R4*(1-(diff(f(eta), eta))^2)-M1*(diff(f(eta), eta)) = 0, diff(diff(theta(eta), eta), eta)+pr1*f(eta)*(diff(theta(eta), eta))-R5*pr1*(diff(f(eta), eta))*theta(eta)+R6*(A1*(diff(f(eta), eta))+B1*theta(eta)) = 0, f(0) = 1, (D(f))(0) = L1+b1*((D@@2)(f))(0), (D(f))(7) = 1, theta(0) = 1+s1*(D(theta))(0), theta(7) = 0], numeric, method = bvp); plots[odeplot](sol2, [eta, ((D@@2)(f))(eta)], color = red); fplt[j] := plots[odeplot](sol2, sol1, [[eta, diff(f(eta), eta)], [eta, diff(f(eta), eta)]], color = K1[j], axes = boxed); tplt[j] := plots[odeplot](sol2, [[eta, theta(eta)]], color = K1[j], axes = normal) end do; plots:-display([seq(fplt[j], j = 1 .. nops(n1))]); plots:-display([seq(tplt[j], j = 1 .. nops(n1))])

Error, (in plots/odeplot) invalid argument: sol1

 

 

 

``

``

sol1(0);

[eta = 0., f(eta) = 1.00000000000000044, diff(f(eta), eta) = .899599635987511914, diff(diff(f(eta), eta), eta) = -.200800728024976643, theta(eta) = 1.18657688243172332, diff(theta(eta), eta) = .373153764863445037]

(3)

sol1(.1)

[eta = .1, f(eta) = 1.08902313464617162, diff(f(eta), eta) = .881503890693141945, diff(diff(f(eta), eta), eta) = -.162309073227910134, theta(eta) = 1.22040489003745489, diff(theta(eta), eta) = .304232440930656767]

(4)

sol1(.2)

[eta = .2, f(eta) = 1.17641763749368966, diff(f(eta), eta) = .866916683092940898, diff(diff(f(eta), eta), eta) = -.130454301210374102, theta(eta) = 1.24759607023709362, diff(theta(eta), eta) = .240488988787701030]

(5)

sol1(.3)

[eta = .3, f(eta) = 1.19045803452309284, diff(f(eta), eta) = .579367537136023514, diff(diff(f(eta), eta), eta) = -.285675511621370782, theta(eta) = 1.18389221591022696, diff(theta(eta), eta) = .146013974567769960]

(6)

sol1(.4)

[eta = .4, f(eta) = 1.40000000000000034, diff(f(eta), eta) = 1.00000000000000022, diff(diff(f(eta), eta), eta) = -0.243774513041384287e-17, theta(eta) = .625958972186505536, diff(theta(eta), eta) = -.314549395236395634]

(7)

sol1(.5)

[eta = .5, f(eta) = 1.37026161183094430, diff(f(eta), eta) = .874752886901313142, diff(diff(f(eta), eta), eta) = .345911467377074400, theta(eta) = .432494259338694842, diff(theta(eta), eta) = -.382764248064397461]

(8)

sol1(.6)

[eta = .6, f(eta) = 1.36678221814533528, diff(f(eta), eta) = .771028661281065508, diff(diff(f(eta), eta), eta) = .407805382194403932, theta(eta) = .876413930517023876, diff(theta(eta), eta) = -.197648778495384870]

(9)

sol1(2)

[eta = 2., f(eta) = 2.66120522956795602, diff(f(eta), eta) = .991532161353848585, diff(diff(f(eta), eta), eta) = 0.251405465681268682e-1, theta(eta) = .635967939441598018, diff(theta(eta), eta) = -.144641270049362308]

(10)

``

``

``

 

``

``

NULL


 

Download staganation_point11.mw
 

``

restart

l := 1:

1

 

1.5

 

.5

 

[blue, green, red, yellow]

(1)

``

for j to nops(A) do R1 := 2*n/(n+1); R2 := 2*p/(n+1); R3 := 2/(n+1); sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R1*(1-(diff(f(eta), eta))^2)-M*(diff(f(eta), eta)) = 0, diff(diff(theta(eta), eta), eta)+pr*f(eta)*(diff(theta(eta), eta))-R2*pr*(diff(f(eta), eta))*theta(eta)+R3*(A[j]*(diff(f(eta), eta))+B*theta(eta)) = 0, f(0) = 1, (D(f))(0) = L+b*((D@@2)(f))(0), (D(f))(20) = 1, theta(0) = 1+s*(D(theta))(0), theta(20) = 0], numeric, method = bvp); plots[odeplot](sol1, [eta, ((D@@2)(f))(eta)], color = red); fplt[j] := plots[odeplot](sol1, [eta, diff(f(eta), eta)], color = K[j], axes = boxed); tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = K[j], axes = normal) end do:

 

 

``

l := 1:

1

 

[0, 1, 1.5]

 

.5

 

[blue, green, red, yellow]

(2)

for j to nops(n1) do R4 := 2*n1[j]/(n1[j]+1); R5 := 2*p1/(n1[j]+1); R6 := 2/(n1[j]+1); sol2 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R4*(1-(diff(f(eta), eta))^2)-M1*(diff(f(eta), eta)) = 0, diff(diff(theta(eta), eta), eta)+pr1*f(eta)*(diff(theta(eta), eta))-R5*pr1*(diff(f(eta), eta))*theta(eta)+R6*(A1*(diff(f(eta), eta))+B1*theta(eta)) = 0, f(0) = 1, (D(f))(0) = L1+b1*((D@@2)(f))(0), (D(f))(7) = 1, theta(0) = 1+s1*(D(theta))(0), theta(7) = 0], numeric, method = bvp); plots[odeplot](sol2, [eta, ((D@@2)(f))(eta)], color = red); fplt[j] := plots[odeplot](sol2, sol1, [[eta, diff(f(eta), eta)], [eta, diff(f(eta), eta)]], color = K1[j], axes = boxed); tplt[j] := plots[odeplot](sol2, [[eta, theta(eta)]], color = K1[j], axes = normal) end do; plots:-display([seq(fplt[j], j = 1 .. nops(n1))]); plots:-display([seq(tplt[j], j = 1 .. nops(n1))])

Error, (in plots/odeplot) invalid argument: sol1

 

 

 

``

``

sol1(0);

[eta = 0., f(eta) = 1.00000000000000044, diff(f(eta), eta) = .899599635987511914, diff(diff(f(eta), eta), eta) = -.200800728024976643, theta(eta) = 1.18657688243172332, diff(theta(eta), eta) = .373153764863445037]

(3)

sol1(.1)

[eta = .1, f(eta) = 1.08902313464617162, diff(f(eta), eta) = .881503890693141945, diff(diff(f(eta), eta), eta) = -.162309073227910134, theta(eta) = 1.22040489003745489, diff(theta(eta), eta) = .304232440930656767]

(4)

sol1(.2)

[eta = .2, f(eta) = 1.17641763749368966, diff(f(eta), eta) = .866916683092940898, diff(diff(f(eta), eta), eta) = -.130454301210374102, theta(eta) = 1.24759607023709362, diff(theta(eta), eta) = .240488988787701030]

(5)

sol1(.3)

[eta = .3, f(eta) = 1.19045803452309284, diff(f(eta), eta) = .579367537136023514, diff(diff(f(eta), eta), eta) = -.285675511621370782, theta(eta) = 1.18389221591022696, diff(theta(eta), eta) = .146013974567769960]

(6)

sol1(.4)

[eta = .4, f(eta) = 1.40000000000000034, diff(f(eta), eta) = 1.00000000000000022, diff(diff(f(eta), eta), eta) = -0.243774513041384287e-17, theta(eta) = .625958972186505536, diff(theta(eta), eta) = -.314549395236395634]

(7)

sol1(.5)

[eta = .5, f(eta) = 1.37026161183094430, diff(f(eta), eta) = .874752886901313142, diff(diff(f(eta), eta), eta) = .345911467377074400, theta(eta) = .432494259338694842, diff(theta(eta), eta) = -.382764248064397461]

(8)

sol1(.6)

[eta = .6, f(eta) = 1.36678221814533528, diff(f(eta), eta) = .771028661281065508, diff(diff(f(eta), eta), eta) = .407805382194403932, theta(eta) = .876413930517023876, diff(theta(eta), eta) = -.197648778495384870]

(9)

sol1(2)

[eta = 2., f(eta) = 2.66120522956795602, diff(f(eta), eta) = .991532161353848585, diff(diff(f(eta), eta), eta) = 0.251405465681268682e-1, theta(eta) = .635967939441598018, diff(theta(eta), eta) = -.144641270049362308]

(10)

``

``

``

 

``

``

NULL


 

Download staganation_point11.mw
 

``

restart

l := 1:

1

 

1.5

 

.5

 

[blue, green, red, yellow]

(1)

``

for j to nops(A) do R1 := 2*n/(n+1); R2 := 2*p/(n+1); R3 := 2/(n+1); sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R1*(1-(diff(f(eta), eta))^2)-M*(diff(f(eta), eta)) = 0, diff(diff(theta(eta), eta), eta)+pr*f(eta)*(diff(theta(eta), eta))-R2*pr*(diff(f(eta), eta))*theta(eta)+R3*(A[j]*(diff(f(eta), eta))+B*theta(eta)) = 0, f(0) = 1, (D(f))(0) = L+b*((D@@2)(f))(0), (D(f))(20) = 1, theta(0) = 1+s*(D(theta))(0), theta(20) = 0], numeric, method = bvp); plots[odeplot](sol1, [eta, ((D@@2)(f))(eta)], color = red); fplt[j] := plots[odeplot](sol1, [eta, diff(f(eta), eta)], color = K[j], axes = boxed); tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = K[j], axes = normal) end do:

 

 

``

l := 1:

1

 

[0, 1, 1.5]

 

.5

 

[blue, green, red, yellow]

(2)

for j to nops(n1) do R4 := 2*n1[j]/(n1[j]+1); R5 := 2*p1/(n1[j]+1); R6 := 2/(n1[j]+1); sol2 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R4*(1-(diff(f(eta), eta))^2)-M1*(diff(f(eta), eta)) = 0, diff(diff(theta(eta), eta), eta)+pr1*f(eta)*(diff(theta(eta), eta))-R5*pr1*(diff(f(eta), eta))*theta(eta)+R6*(A1*(diff(f(eta), eta))+B1*theta(eta)) = 0, f(0) = 1, (D(f))(0) = L1+b1*((D@@2)(f))(0), (D(f))(7) = 1, theta(0) = 1+s1*(D(theta))(0), theta(7) = 0], numeric, method = bvp); plots[odeplot](sol2, [eta, ((D@@2)(f))(eta)], color = red); fplt[j] := plots[odeplot](sol2, sol1, [[eta, diff(f(eta), eta)], [eta, diff(f(eta), eta)]], color = K1[j], axes = boxed); tplt[j] := plots[odeplot](sol2, [[eta, theta(eta)]], color = K1[j], axes = normal) end do; plots:-display([seq(fplt[j], j = 1 .. nops(n1))]); plots:-display([seq(tplt[j], j = 1 .. nops(n1))])

Error, (in plots/odeplot) invalid argument: sol1

 

 

 

``

``

sol1(0);

[eta = 0., f(eta) = 1.00000000000000044, diff(f(eta), eta) = .899599635987511914, diff(diff(f(eta), eta), eta) = -.200800728024976643, theta(eta) = 1.18657688243172332, diff(theta(eta), eta) = .373153764863445037]

(3)

sol1(.1)

[eta = .1, f(eta) = 1.08902313464617162, diff(f(eta), eta) = .881503890693141945, diff(diff(f(eta), eta), eta) = -.162309073227910134, theta(eta) = 1.22040489003745489, diff(theta(eta), eta) = .304232440930656767]

(4)

sol1(.2)

[eta = .2, f(eta) = 1.17641763749368966, diff(f(eta), eta) = .866916683092940898, diff(diff(f(eta), eta), eta) = -.130454301210374102, theta(eta) = 1.24759607023709362, diff(theta(eta), eta) = .240488988787701030]

(5)

sol1(.3)

[eta = .3, f(eta) = 1.19045803452309284, diff(f(eta), eta) = .579367537136023514, diff(diff(f(eta), eta), eta) = -.285675511621370782, theta(eta) = 1.18389221591022696, diff(theta(eta), eta) = .146013974567769960]

(6)

sol1(.4)

[eta = .4, f(eta) = 1.40000000000000034, diff(f(eta), eta) = 1.00000000000000022, diff(diff(f(eta), eta), eta) = -0.243774513041384287e-17, theta(eta) = .625958972186505536, diff(theta(eta), eta) = -.314549395236395634]

(7)

sol1(.5)

[eta = .5, f(eta) = 1.37026161183094430, diff(f(eta), eta) = .874752886901313142, diff(diff(f(eta), eta), eta) = .345911467377074400, theta(eta) = .432494259338694842, diff(theta(eta), eta) = -.382764248064397461]

(8)

sol1(.6)

[eta = .6, f(eta) = 1.36678221814533528, diff(f(eta), eta) = .771028661281065508, diff(diff(f(eta), eta), eta) = .407805382194403932, theta(eta) = .876413930517023876, diff(theta(eta), eta) = -.197648778495384870]

(9)

sol1(2)

[eta = 2., f(eta) = 2.66120522956795602, diff(f(eta), eta) = .991532161353848585, diff(diff(f(eta), eta), eta) = 0.251405465681268682e-1, theta(eta) = .635967939441598018, diff(theta(eta), eta) = -.144641270049362308]

(10)

``

``

``

 

``

``

NULL


 

Download staganation_point11.mw

 

in this program im trying to combine the result, but it showing some error can help me please

 

 

 

Hi everybody,

So today is 10-28-2016 and I explored Leyland Numbers for the first time, on Maple.  Please see my example file and let me know what your impression is.

x_to_the_yth_power_and_y_to_the_xth_power_take_4.mw

x_to_the_yth_power_and_y_to_the_xth_power_take_4.pdf

I have included a .pdf file so that the caual internet observer can also be aware of this information.

Regards,
Matt

 

> restart;

with(plots);

pr := .72; p := 0; n := [.5, 1, 1.5]; s := 0; a := .2; b := 0; L := [red, blue, green]; l := 0; k := 1;

for j to nops(n) do R1 := 2*n[j]/(1+n[j]); R2 := 2*p/(1+n);

sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R1*(1-(diff(f(eta), eta))^2) = 0, diff(diff(theta(eta), eta), eta)+pr*k*f(eta)*(diff(theta(eta), eta))+R2*pr*k*(diff(f(eta), eta))*theta(eta)+(2*(a*(diff(f(eta), eta))+b*theta(eta)))/(1+n[j]) = 0, f(0) = 1, (D(f))(0) = b*((D@@2)(f))(0), (D(f))(1.8) = 0, theta(0) = 1+s*(D(theta))(0), theta(1.8) = 1], numeric, method = bvp);

fplt[j] := plots[odeplot](sol1, [eta, diff(diff(f(eta), eta), eta)], color = L[j], axes = boxed); tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = L[j], axes = normal) end do; plots:-display([seq(fplt[j], j = 1 .. nops(n))]);

plots:-display([seq(tplt[j], j = 1 .. nops(n))]);

 

staganation_point1.mw
 

can we chage the axis sir ?? like  f'' vs eta to f'' vs lambda.

``

restart

l := 1:

1

 

1.5

 

.5

 

[blue, green, red, yellow]

(1)

``

for j to nops(p) do R1 := 2*n/(n+1); R2 := 2*p[j]/(n+1); R3 := 2/(n+1); sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R1*(1-(diff(f(eta), eta))^2)-M*(diff(f(eta), eta)) = 0, diff(diff(theta(eta), eta), eta)+pr*f(eta)*(diff(theta(eta), eta))-R2*pr*(diff(f(eta), eta))*theta(eta)+R3*(A*(diff(f(eta), eta))+B*theta(eta)) = 0, f(0) = 1, (D(f))(0) = L+b*((D@@2)(f))(0), (D(f))(7) = 1, theta(0) = 1+s*(D(theta))(0), theta(7) = 0], numeric, method = bvp); plots[odeplot](sol1, [eta, ((D@@2)(f))(eta)], color = red); fplt[j] := plots[odeplot](sol1, [eta, f(eta)], color = K[j], axes = boxed); tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = K[j], axes = normal); fplt[j] := plots[odeplot](sol1, [eta, diff(f(eta), eta)], color = K[j], axes = boxed) end do:

 

 

plots:-display([seq(fplt[j], j = 1 .. nops(n))]);

 

sol1(0)

sol1(0)

(2)

sol1(.1)

[eta = .1, f(eta) = 1.05958091104306206, diff(f(eta), eta) = .643210624614908300, diff(diff(f(eta), eta), eta) = .881482678165403044, theta(eta) = .623284688471349546, diff(theta(eta), eta) = -.578039450700496560]

(3)

sol1(.2)

[eta = .2, f(eta) = 1.12800452943200891, diff(f(eta), eta) = .722346769554029544, diff(diff(f(eta), eta), eta) = .706526135439307756, theta(eta) = .568123251856343492, diff(theta(eta), eta) = -.525530979400813946]

(4)

sol1(.3)

[eta = .3, f(eta) = 1.20351830506746449, diff(f(eta), eta) = .785511903074783246, diff(diff(f(eta), eta), eta) = .561442941644520022, theta(eta) = .518103974464032668, diff(theta(eta), eta) = -.475257424178228970]

(5)

sol1(.4)

[eta = .4, f(eta) = 1.28466826824405134, diff(f(eta), eta) = .835505660630676662, diff(diff(f(eta), eta), eta) = .442470716586289281, theta(eta) = .472985640642506311, diff(theta(eta), eta) = -.427567049032814172]

(6)

sol1(.5)

[eta = .5, f(eta) = 1.37026161183094430, diff(f(eta), eta) = .874752886901313142, diff(diff(f(eta), eta), eta) = .345911467377074400, theta(eta) = .432494259338694842, diff(theta(eta), eta) = -.382764248064397461]

(7)

sol1(.6)

[eta = .6, f(eta) = 1.36678221814533528, diff(f(eta), eta) = .771028661281065508, diff(diff(f(eta), eta), eta) = .407805382194403932, theta(eta) = .876413930517023876, diff(theta(eta), eta) = -.197648778495384870]

(8)

sol1(2)

[eta = 2., f(eta) = 2.66120522956795602, diff(f(eta), eta) = .991532161353848585, diff(diff(f(eta), eta), eta) = 0.251405465681268682e-1, theta(eta) = .635967939441598018, diff(theta(eta), eta) = -.144641270049362308]

(9)

``

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``


 

Download staganation_point1.mw

 

 

 

 

 

http://www.sciencedirect.com/science/article/pii/S100757041300508X> restart;
> l := 1; p := 1; A := .5; B := .5; pr := 1; n := [.5, 1, 1.5]; M := 0; b := .5; L := 0; s := .5; K := [blue, green];
                                      1
                                [0.5, 1, 1.5]
                                [blue, green]

> for j to nops(n) do R1 := 2*n[j]/(n[j]+1); R2 := 2*p/(n[j]+1); R3 := 2/(n[j]+1);

sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R1*(1-(diff(f(eta), eta))^2)-M*(diff(f(eta), eta)) = 0, diff(diff(theta(eta), eta), eta)+pr*f(eta)*(diff(theta(eta), eta))-R2*pr*(diff(f(eta), eta))*theta(eta)+R3*(A*(diff(f(eta), eta))+B*theta(eta)) = 0, f(0) = 1, (D(f))(0) = L+b*((D@@2)(f))(0), (D(f))(7) = 1, theta(0) = 1+s*(D(theta))(0), theta(7) = 0], numeric, method = bvp);

plots[odeplot](sol1, [eta, ((D@@2)(f))(eta)], color = red);

fplt[j] := plots[odeplot](sol1, [eta, diff(diff(f(eta), eta), eta)], color = K[j], axes = boxed); fplt[j] := plots[odeplot](sol1, [eta, f(eta)], color = K[j], axes = boxed);

tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = K[j], axes = normal) end do;

plots:-display([seq(fplt[j], j = 1 .. nops(n))]);

plots:-display([seq(fplt[j], j = 1 .. nops(n))]);

plots:-display([seq(tplt[j], j = 1 .. nops(n))]);
http://www.sciencedirect.com/science/article/pii/S100757041300508X

Dear sir 

I am trying to plot the following link paper graphs for practice but I getting the plots for only one set of values here in this paper they plotted many so if you dont muned can help in this case. For example in this first graph named as Fig.1. please can you do this favour... and the paper link is  http://www.sciencedirect.com/science/article/pii/S100757041300508X

 

Hi Mapleprimes,

I have made this little procedure with Maple. 

check_g_conjecture_10.pdf

similar to this next one check_g_conjecture_10.mw

This may be worth a look.

Regards,

Matthew

P.S.   see  https://en.wikipedia.org/wiki/Goldbach%27s_conjecture

In My Humble Opinion, Wikipedia is a good crowd sourced resource.

 

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