## 155 Reputation

11 years, 205 days

## display pde in desired form...

Maple 13

How to display the result in the desired form in partial differential equation and also collect the same terms

i am attaching sample codes

restart:
with(DETools):
P[o](z):=C[o]*exp(lambda*z)+D[o]*exp(-lambda*z):
u[o](r,z):=(1-r^2)*diff(P[o](z),z):
v[o](r,z):=(2*r-r^3)*diff(P[o](z),z,z):
A1:=P[o](z)*u[o](r,z):
# we want the result out put  like this
A1 := lambda*(C[o]^2*exp(2*lambda*z)-D[o]^2*exp(-2*lambda*z))*(1-r^2):
A2:=P[o](z)*(1+r^2)+v[o](r,z)+A1:
#we want the  resultant output like this
A2:=lambda^2*(C[o]*exp(lambda*z)+D[o]*exp(-lambda*z))*(1+r^2+2*r-r^3)+A1:

## Differential equations solving ...

Maple 13

Any one can help me to solve the differential equations using maple to get the velocities u ,v and pressure p for the problem mentioned below

## How to convert Matlab codes to Maple co...

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

## how to get the output of the plots in ro...

Maple 13

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(`&delta;1`), typeset(conjugate(`&Delta;p`))],
title=typeset("Effect of ", ''alpha'', " when ", Gamma,"2=", Gamma2)
),
Gamma2 in [10,20,30,40,50,-10]
)
]
)
);

## how to remove error in plot display...

Maple 13

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);

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