Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

x: =Matrix([[a1,a2],[a3,a4]])

after some calculation,

assign(%)

a1 etc have value,

how to make a1,a2,a3,a4 back to variable in maple 12?

How to calculate floor(10^(10^(10^(10^(10^(-10^10))))))? My simpleminded try is

Error, numeric exception: underflow
PS. I think that is about 10^(10^10).

m := Matrix([[a1,a2,a3],[a4,a5,a6],[a7,a8,a9]]);

m2 := Determinant(m-Matrix([[1,0,0],[0,1,0],[0,0,1]]));

1. which family of polynomials do m2 belong to?

2. how to analyze m2?

What´s the error here??????

Solução do Sistema de EDO's por Transformada de Laplace

 

restart

with(inttrans):

eq1 := diff(x(t), t)+(2.2*x(t)*y(t)+0.5e-1*x(t)/(5+0.5e-1*t)) = 0;

diff(x(t), t)+2.2*x(t)*y(t)+0.5e-1*x(t)/(5+0.5e-1*t) = 0

(1)

eq2 := diff(y(t), t)+(2.2*x(t)*y(t)-(0.5e-1*(0.25e-1-y(t)))/(5+0.5e-1*t)) = 0;

diff(y(t), t)+2.2*x(t)*y(t)-0.5e-1*(0.25e-1-y(t))/(5+0.5e-1*t) = 0

(2)

eq3 := diff(z(t), t)-2.2*x(t)*y(t)+0.5e-1*z(t)/(5+0.5e-1*t) = 0;

diff(z(t), t)-2.2*x(t)*y(t)+0.5e-1*z(t)/(5+0.5e-1*t) = 0

(3)

EQ := [eq1, eq2, eq3]:

for i to 3 do La[i] := laplace(EQ[i], t, s) end do;

s*laplace(x(t), t, s)-1.*x(0.)+2.200000000*laplace(x(t)*y(t), t, s)+laplace(x(t)/(100.+t)^1., t, s) = 0.

 

-1.*y(0.)-0.2500000000e-1*(exp(100.*s))^1.*Ei(1., 100.*s)^1.+1.*s^1.*laplace(y(t), t, s)^1.+2.200000000*laplace(x(t)^1.*y(t)^1., t, s)+1.*laplace(y(t)^1./(100.+1.*t)^1., t, s) = 0.

 

s*laplace(z(t), t, s)-1.*z(0.)-2.200000000*laplace(x(t)*y(t), t, s)+laplace(z(t)/(100.+t)^1., t, s) = 0.

(4)

LL := subs({laplace(x(t), t, s) = X, laplace(y(t), t, s) = Y, laplace(z(t), t, s) = Z}, [La[1], La[2], La[3]]);

[s*X-1.*x(0.)+2.200000000*laplace(x(t)*y(t), t, s)+laplace(x(t)/(100.+t)^1., t, s) = 0., -1.*y(0.)-0.2500000000e-1*(exp(100.*s))^1.*Ei(1., 100.*s)^1.+1.*s^1.*Y^1.+2.200000000*laplace(x(t)*y(t), t, s)+1.*laplace(y(t)/(100.+t)^1., t, s) = 0., s*Z-1.*z(0.)-2.200000000*laplace(x(t)*y(t), t, s)+laplace(z(t)/(100.+t)^1., t, s) = 0.]

(5)

sol := solve(LL, [X, Y, Z]):

assign(sol):

SOLS[X, Y, Z]:

SOLT := map(invlaplace, [X, Y, Z], s, t);

[-2.200000000*(int(x(_U1)*y(_U1), _U1 = 0. .. t))-1.*(int(x(_U1)/(100.+_U1), _U1 = 0. .. t))+x(0), -1.*(int(y(_U1)/(100.+_U1), _U1 = 0. .. t))-2.200000000*(int(x(_U1)*y(_U1), _U1 = 0. .. t))+y(0)+0.2500000000e-1*ln(1.+0.1000000000e-1*t), 2.200000000*(int(x(_U1)*y(_U1), _U1 = 0. .. t))-1.*(int(z(_U1)/(100.+_U1), _U1 = 0. .. t))+z(0)]

(6)

SOLTT := evalf(subs({x(0) = 0.5e-1, y(0) = 0, z(0) = 0}, SOLT));

[-2.200000000*(int(x(_U1)*y(_U1), _U1 = 0. .. t))-1.*(int(x(_U1)/(100.+_U1), _U1 = 0. .. t))+0.5e-1, -1.*(int(y(_U1)/(100.+_U1), _U1 = 0. .. t))-2.200000000*(int(x(_U1)*y(_U1), _U1 = 0. .. t))+0.2500000000e-1*ln(1.+0.1000000000e-1*t), 2.200000000*(int(x(_U1)*y(_U1), _U1 = 0. .. t))-1.*(int(z(_U1)/(100.+_U1), _U1 = 0. .. t))]

(7)

xx := evalc(Re(SOLTT[1]));

-2.200000000*(int(x(_U1)*y(_U1), _U1 = 0. .. t))-1.*(int(x(_U1)/(100.+_U1), _U1 = 0. .. t))+0.5e-1

(8)

yy := evalc(Re(SOLTT[2]));

0.2500000000e-1*ln(abs(1.+0.1000000000e-1*t))-1.*(int(y(_U1)/(100.+_U1), _U1 = 0. .. t))-2.200000000*(int(x(_U1)*y(_U1), _U1 = 0. .. t))

(9)

zz := evalc(Re(SOLTT[3]));

2.200000000*(int(x(_U1)*y(_U1), _U1 = 0. .. t))-1.*(int(z(_U1)/(100.+_U1), _U1 = 0. .. t))

(10)

plot([xx, yy, zz], t = 0 .. 500, legend = [x, y, z]);

Warning, expecting only range variable t in expression -2.200000000*int(x(_U1)*y(_U1),_U1 = 0. .. t)-1.*int(x(_U1)/(100.+_U1),_U1 = 0. .. t)+.5e-1 to be plotted but found names [_U1, x, y]

 

 

NULL

NULL


Download laplace.mw

Dear Friends

I have a problem in CPU time in MAPLE.

I write the codes in maple related to the nonlinear heat conduction problem in one dimension by Collocation method, but after 30 minutes no solution has been observed!!!

My codes are for N=4!, i.e., I have 25 equations with 25 unknowns!!!

If MAPLE can not solve this simple system, How can I solve 3 dimensional pdes by N=9,

In this case, I have 1000 equations with 1000 unknowns!!!

please help me and suggest me a fast iterative solver.

I should remark that my problem is stated in this paper

http://www.sciencedirect.com/science/article/pii/S1018364713000025

If there exist any other suitable method, I will be happy to receive any support.

 

With kind regards,

Emran Tohidi.

 

> restart;
> Digits := 20; N := 4; st := time(); u := sum(sum(a[m, n]*x^m*t^n, m = 0 .. N), n = 0 .. N); u := unapply(u, x, t); ut := diff(u(x, t), `$`(t, 1)); ut := unapply(ut, x, t); ku := simplify(1+u(x, t)^2); ku := unapply(ku, x, t); ux := diff(u(x, t), `$`(x, 1)); ux := unapply(ux, x, t); K := ku(x, t)*ux(x, t); K := unapply(K, x, t); Kx := diff(K(x, t), `$`(x, 1)); Kx := unapply(Kx, x, t); f := proc (x, t) options operator, arrow; x*exp(t)*(1-2*exp(2*t)) end proc;
print(`output redirected...`); # input placeholder
> S1 := {seq(u(i/N, 0)-i/N = 0, i = 0 .. N)}; S2 := {seq(u(0, j/N) = 0, j = 1 .. N)}; S3 := {seq(u(1, j/N)+ux(1, j/N)-2*exp(j/N) = 0, j = 1 .. N)}; S4 := {seq(seq(Kx(i/N, j/N)+f(i/N, j/N)-ut(i/N, j/N) = 0, i = 1 .. N-1), j = 1 .. N)}; S := `union`(`union`(`union`(S1, S2), S3), S4); sol := DirectSearch:-SolveEquations([op(S)], tolerances = 10^(-4), evaluationlimit = 1000000);
print(`output redirected...`); # input placeholder
> assign(sol);
%;
> u(x, t);
> CPUTIME := time()-st;
plot3d(u(x, t) - x exp(t), x = 0 .. 1, t = 0 .. 1)

Hello,

I just bought and installed "The mathematical Survival Kit" but I can't figure out how does it work

Anybody can help?

 

Thanaks

Martina

What is the difference between the "old" Maplet format and the "new" Möbius Project App format? Is the Möbius Project just a new name for writing Maplets? Is the programming different; are the mechanics of putting the file in a form to be used by students different; does the file containing the program that can be directly run by students have a different format and extension; are the kinds of things students see different? Is the Maplets function on the way to being discontinued in favor of the Möbius Apps?

I cannot find anything in the documentation for either format that relates it to the other format, although the general description of the output seems entirely the same.

Hi:

how find the coefficients C1,C2?
q(0)=0,D(q)(0)=0

q(T) := sin(T)*_C2+cos(T)*_C1-(1/3000)*Pi*(4012562293500*Pi^3*cos(T)^3-32100498340000*Pi^3*cos(T)^2-3009421720125*Pi^3*cos(T)+16050249170000*Pi^3+435778855000*Pi*cos(T)^2-217889427500*Pi-3539762622):

We know that the set f:={(1,2),(2,a),(3,b)} can introduce a function from {1,2,3} to {2,a,b}. I want Maple to know f as a function. Is this job possible at Maple? I thought to find the Cartesian product of above latter sets and then try to select "f" as one of its subset but this did not help me to force Maple to take "f" as a function. Indeed, I want to work with this kind of function (like plotting and doing f+g, f-g, fog for two functions for example).

Thanks for your time and help.

 

how to plot tail of normal distribution

would like to see the shape of tail of distribution

 Hi all,

i want to solve a system of differential equations in maple with "dsolve, numeric",

i got th error message: "Error, (in f) unable to store in Matrix ..."

what is the problem?

thanks a lot

What is the command to get a sequence of the first twenty prime numbers

why system inconsistent 

when only want to obtain a equation H

in terms of a1 , a3, b2, b3, c1, c2, x1, x2, lambda

pdsolve([
Diff(H(x1,x2,lambda), x1) = a1*x1 + a3*lambda,
Diff(H(x1,x2,lambda), x2) = b2*x2 + b3*lambda,
Diff(H(x1,x2,lambda), lambda) = c1*x1 + c2*x2
], H(x1,x2,lambda));

Hi all. I am using Maple 18.

1. Does Maple only output an answer, or can it be made to display the steps it took to achieve the result, in a way that is logical and understandable by the user? For example, I would like to see it display steps when integrating or differentiating, or dividing a polynomial by another polynomial. Basically any process that involve simplifyinf or factorisation.

2. I am trying to divide x^2 + 5x + 9 by x+2, but all Maple displays is the expression

How can I make it do the polynomial division and output the steps it took? I tried using simplify and evaluate from the context menu but the output is still just the expression.

3. Has something happened to this site? It was working fine in Opera until two days ago, and has sinmce started displaying "Error generating page" where the replies to questions should be. No problems with the "posts" section, only in the "questions" section.

Thanks in advance.

 

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