Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hi Maple users :)

do you know if exists a Maple package in order to perform a Panel method, for instance in the Hess-Smith version, for solving incompressible potential flow over thick 2d and 3d airfoil geometries?

Thank in advance for the help.

solve Differential equation "a-y=y' bc" use maple 17

the result is y(x)=a+_C1e^-(1/bc)

but the correct result  isn't y(x)=a-_C1e^-(1/bc) ?

Thank you in advance for your help

 

Hi :)

I have a Macbook Air running on OS X Mavericks. I am using Maple16.

I created a procedure, which construct two keys. Each of those keys consists of a list containing two elements. That is two primes. So at the end of my procedure I included the following code in order to write my data to a file:

> pkey := fopen(keyFile, WRITE, TEXT);
                      pkey:=1
> writedata(pkey, publicKey);
> fclose(pkey);

The problem is that I can't find the created file "keyFile".

So I tried breaking the problem down. I created a List and wanted to write that list in a textfile in a specific folder:

> L := [1, 2, 3];
> fd := fopen("Users\\****\\Desktop\\fdtest.txt", WRITE, TEXT);
                              fd:=1
> fprintf(fd, "This is a test");
                              14
> fclose(fd);

But this did not work either. It seems like the file fdtest.txt never gets created. This happens in general when I use fopen().

Thank you in advance for your help

Schloemilch

 

 

I have a matrix then I need to plot its columns as curves on one plot.

I'm interested in doing some experimental mathematics using the PSLQ integer relation algorithm.  The only third-party program for doing PSLQ problems I've been able to find is a GNU C++ program with a less-than-user-friendly command-line interface.  I've heard that Maple implements PSLQ and I like the symbolic input and presentation it offers as a CAS, but I can't find any information on which alternative types of Maple 18 make the PSLQ algorithm available.

f1 := expand((a1*x^2+b1*x+c1)^n);
f2 := a1*x^2+b1*x+c1;

solve([coeff(f1, x, 4) = coeff(f2, x, 4),
coeff(f1, x, 3) = coeff(f2, x, 3),
coeff(f1, x, 2) = coeff(f2, x, 2),
coeff(f1, x, 1) = coeff(f2, x, 1),
coeff(f1, x, 0) = coeff(f2, x, 0)], [a1,b1,c1,d1]);

how to convert decimal number into given decimal number like algebra

for example, convert 191.715 , given a=12.2, b=3.5

how to find this a^2 + b^3

Hello, I am a student typing up my homework assignments with maple, and I am takinng Inferential Statistics.  I can't figure out how to make the bar over a variable, so I can note the average.  It is just a line over a letter.  Kind of when notating a vector without the arrow.  It would be very helpful because I can't figure out how to make that symbol, it is not listed on the symbols list on the left side.

Thanks!

 

hi.i encountered this erroe  [Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system] with solving set of differential equation.please help me.thanks a lot  

dsys3 := {`1`*h1(theta)+`1`*(diff(h1(theta), theta, theta))+`1`*(diff(h2(theta), theta))+`1`*(diff(h2(theta), theta, theta, theta))+`1`*h3(theta)+`1`*(diff(h3(theta), theta, theta))+`1`*(diff(h1(theta), theta, theta, theta, theta)) = 0, `1`*h2(theta)+`1`*(diff(h2(theta), theta, theta, theta, theta))+`1`*(diff(h2(theta), theta, theta))+`1`*(diff(h1(theta), theta))+`1`*(diff(h1(theta), theta, theta, theta))+`1`*(diff(h3(theta), theta))+`1`*(diff(h3(theta), theta, theta, theta)) = 0, h3(theta)^5*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+(diff(h3(theta), theta, theta))*h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+(diff(h3(theta), theta, theta, theta, theta))*h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+h1(theta)*h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+(diff(h1(theta), theta, theta))*h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+(diff(h2(theta), theta))*h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+(diff(h2(theta), theta, theta, theta))*h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+h3(theta)^4*(diff(h2(theta), theta, theta, theta, theta, theta, theta))*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)-beta*h3(theta)^3*`1`-chi*ln(h3(theta))^2*`1`/kappa-chi*`1`/kappa-2*chi*ln(h3(theta))*`1`/kappa = 0, h1(0) = 0, h1(1) = 0, h2(0) = 0, h2(1) = 0, h3(0) = 1, h3(1) = 1, ((D@@1)(h1))(0) = 0, ((D@@1)(h1))(1) = 0, ((D@@1)(h2))(0) = 0, ((D@@1)(h2))(1) = 0, ((D@@1)(h3))(0) = 0, ((D@@1)(h3))(1) = 0, ((D@@2)(h3))(0) = 0, ((D@@2)(h3))(1) = 0}; dsol5 := dsolve(dsys3, 'maxmesh' = 600, numeric, output = listprocedure);
%;
Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

 

Hi Maple friends. :)

I would like to graph and solve: 2*sin(2 x)=1 for the interval 0<=x<=360. My textbook gives the answers of x=15, 75, 195 and 225.

But I get an error messages:

plot(2*sin(2*x) = 1, x = 0 .. 360);
Error, invalid input: plot expects its 1st argument, p, to be of type {array, list, rtable, set, algebraic, procedure, And(`module`, appliable)}, but received 2*sin(2*x) = 1

solve(2*sin(2*x) = 1, x = 0 .. 360);
Error, invalid input: too many and/or wrong type of arguments passed to solve; first unused argument is x = 0 .. 360

Any help would be appreciated! Thanks in advance.

 

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)

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