Maple 13 Questions and Posts

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

Any one can help me to convert matlab codes to maple.Matlab_code.mw
 

%Finite element method code for solving bvp nonlinear ODEs%

% u''+uu'-u=exp(2x), u(0)= 1, u(1)=e     %

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function FEM_Code()

clear all; close all; clc

n=5;                     % NO of element

nn=n+1;                  % No of nodes

lgth=1;                  % Domain length

he=lgth/n;               % lenth of each elemnet

x=[0:he:lgth];           % Data point for independant variable

AC=0.00005;              % Accuracy

F=zeros(nn,1);           % Initialization

F(1)=exp(0); F(nn)=exp(1);  % Boundary conditions

 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Direct Iterative process to handle nonlinear problem

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

c=1.0;

count=0;                   % Initializations for count for iterations

tic                        % Time start

while (c>0)

        [F1]=assembly(F,n,he);

          c=0.0;

          for i=1:nn

            if (abs(F(i)-F1(i))>AC)

                 c=c+1;

                 break;

            end

          end

         F=F1;

         count=count+1;

end

  disp('Hence solution=:');

  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  % Output for prinmary and secondary variables %%%

  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  diff=abs(F-exp(x)');

  fprintf('No of element=%d\n',n)

  disp('      x       FEM          Exact       Error')

  disp([x',F,exp(x)',diff])

  fprintf('No of iterations=%d\n',count)

  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  %%% Ploting of primary variable %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  

  plot(x,F,'--rs','Linewidth',2)

  xlabel('x')

  ylabel('u(x)')

  title('solution plot to given BVP')

  toc                                % given totlal time

  

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% Derivative of element matrix and Assembly%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

 

function [F1]=assembly(F,n,he)

nn=n+1;

k = zeros(nn,nn);               % Initialization of main Matrix

R = zeros(nn,1);                % Initialization of RHS Matrix

syms x                          % x as symbolic variable

s=[1-x/he,x/he];                % linear shape function

ds=diff(s,x);                   % Differentiations of shape function

lmm =[];

for i=1:n

    lmm=[lmm;[i,i+1]];          % connectvity Matrix

end

for i=1:n

    lm=lmm(i,:);

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    %%% Generation of Element Matrix k11 and RHS Matrix f1%%%%%%%%%%

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    k11=-int(ds'*ds,x,0,he)+(int(s'*ds*s(1),x,0,he)*F(lm(1))...

        +int(s'*ds*s(2),x,0,he)*F(lm(2)))-int(s'*s,x,0,he);

    f1 = int(exp(2*(x+(i-1)*he))*s',x,0,he);

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    %%% Assembly accroding to connectivity Matrix%%%%%%%%%%%%%%%%%%%%

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    

    k(lm,lm) = k(lm,lm) + k11;

    R(lm) = R(lm) + f1;

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% Imposing Boundary Conditions %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

 

k(1,:) = 0.0; k(nn,:) = 0.0;

k(1,1) = 1.0; k(nn,nn) = 1.0;

R(1,1) = F(1); R(nn,1) = F(nn);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% Solution of equations (F1) %%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

 

d = k\R;           % better than using inverse k*R

F1 = d;

end

 

    

 

                                

 

 

 

  

        

      

 

 

 

 

 

 


 

Download Matlab_code.mw

i am attaching the codes and file. i will be thankful to you .

How can I activate my maple 13?

I have no activatIon left but installed maple

once

My purchase Code is BNN7VMT4BPFN7ESG

Thank. You 


 

restart

" S3:=proc(psi) [[[cos(psi),-sin(psi),0],[sin(psi),cos(psi),0],[0,0,1]]]:  end  proc ;   S1:=proc(`ϕ`)  [[[1,0,0],[0,cos(`ϕ`),-sin(`ϕ`)],[0,sin(`ϕ`),cos(`ϕ`)]]]:   end proc;"

proc (psi) Matrix(3, 3, {(1, 1) = cos(psi), (1, 2) = -sin(psi), (1, 3) = 0, (2, 1) = sin(psi), (2, 2) = cos(psi), (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1}) end proc

 

proc (`ϕ`) Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = cos(psi), (2, 3) = -sin(psi), (3, 1) = 0, (3, 2) = sin(psi), (3, 3) = cos(psi)}) end proc

(1)

``

S3(uu)

Matrix([[cos(uu), -sin(uu), 0], [sin(uu), cos(uu), 0], [0, 0, 1]])

(2)

S1(uu)

Matrix([[1, 0, 0], [0, cos(psi), -sin(psi)], [0, sin(psi), cos(psi)]])

(3)

``


 

Download test3.mw

Way i get the wrong output with procedure S1(uu)
 

arrow([u1, u2, u3], shape = cylindrical_arrow, length = sqrt(LinearAlgebra:-Transpose(f0).f0), color = [red, black, green]):

Why i get this error

Error: the number of colours in the COLOUR structure is not sufficient.Error: the number of colours in the COLOUR structure is not sufficient.Error: the number of colours in the COLOUR structure is not sufficient.Error: the number of colours in the COLOUR structure is not sufficient.Error: the number of colours in the COLOUR structure is not sufficient.Error: the number of colours in the COLOUR structure is not sufficient.

I am trying to solve a second order differential equation but getting error. The differential equation valid for r>0.

 

Vr.mw

I am trying to solve system of differential equation as shown in file attached. The differentail eqaution has peicewise function for t=8*n and t not equal to 8*n where n is a positive integer. but i am getting error. please help.

 

 

problem30.mw

Hello everyone! I have just started to using Maple 13. I want to solve complex eauation systems.

When I am working on Maple, If I write simple mathematical calculation and then press right click, the context menu open. However, I want to use solve command. Therefore I wrote an eauation after than press right click the context menu will not open. 

What is the reason of this problem? 

Integral is not evaluated. 

 

PROBLE_13.mw

please I need the code to calculate the convergence order of a multipoint iterative method to solve nonlinear equation systems.

 

my email is: yjmsigma@gmail.com

 

In the first one I used hypergeometric function where the number is converged. Now using the series expansion of hypergeometric function I rewrite the equation as in the 2nd and 3rd case. But here it is not converging. I expect the same answer as in the first case i.e 0.14042. Thank you

 

problem2.mw

In the following problem at two example are given. For Z=2 the sum is converging whereas at Z=4 it is not converging. Thank you

 

PROBLEM.mw

any one can help me to get the output of the plot in 3 rows and 2 columns here is my codes. thanks in advance.

 restart;
  h:=z->1-(delta2/2)*(1 + cos(2*(Pi/L1)*(z - d1 - L1))):
  K1:=((4/h(z)^4)-(sin(alpha)/Gamma2)-h(z)^2+Nb*h(z)^4):
  lambda:=unapply(Int(K1,z=0..1), Gamma2):
  L1:=0.2:
  d1:=0.2:
  alpha:=Pi/6:
  with(plots):
  display
  ( Vector[row]
    ( [ seq
        ( plot
          ( [ seq
              ( eval(lambda(Gamma2), Nb=j),
                j in [0.1,0.2,0.3]
              )
            ],
            delta2=0.02..0.1,
            legend=[Nb=0.1,Nb=0.2,Nb=0.3],
            labels=[typeset(`δ1`), typeset(conjugate(`Δp`))],
            title=typeset("Effect of ", ''alpha'', " when ", Gamma,"2=", Gamma2)
          ),
          Gamma2 in [10,20,30,40,50,-10]
        )
      ]
    )
  );
 

Hellow ,

any body can help me to remove the error from the plot, here is my codes .

Note. 1. *Title {Effect of alpha when 'Gamma2'=Gamma2}

2. *on the y axis i want  bar(deltap)

 

 

 

restart;

 

 

h:=z->1-(delta2/2)*(1 + cos(2*(Pi/L1)*(z - d1 - L1))):
K1:=((4/h(z)^4)-(sin(alpha)/Gamma2)-h(z)^2+Nb*h(z)^4):
lambda:=unapply(Int(K1,z=0..1), Gamma2):
L1:=0.2:
d1:=0.2:
alpha:=Pi/6:
plots:-display(Vector[row]([seq(plot([seq(eval(lambda(Gamma2), Nb=j), j=[0.1,0.2,0.3])], delta2=0.02..0.1, legend=[Nb=0.1,Nb=0.2,Nb=0.3],labels = ["d1 ", "Dp"],labelfont = ["SYMBOL", 12], title=(Effect of alpha when 'Gamma2'=Gamma2)), Gamma2=[10,20,30])]),axes=boxed);
 

how to adjust the height and width of plot in maple 13

plot( x[3]^5, caption = typeset("\n A plot of %1.", x[3]^5), captionfont=[times, 20] );

hellow,

can any body help me to  increase the size of the caption in maple plot

plot( x[3]^5, caption = typeset("A plot of %1.", x[3]^5) );

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