Hi

I have a nonlinear PDEs, solved using finite difference in the square

I get the following nonlinear system of equation. Is there any idea how correct the code and display the solution.

I will appreciate any help in this question.

restart;
n:=100;
h:=1/(n+1);

# Boundary condition

for j from 0 by 1  to n+1 do
u[0, j] = 0;
u[n+1, j] = 0;
u[j, 0] = 0;
u[j, n+1] = 0 ;
end do;
## Loop for interior point in the square
for i from 1 by 1 to  n do
for j from 1 by 1 to  n do
(u[i+1, j]-u[i, j])*(u[i+1, j]-2*u[i, j]+u[i-1, j])+h*(u[i, j+1]-2*u[i, j]+u[i, j-1]) = 0;
end do;
end do;
 

How can I solve this system of equations with unknown u[i,j], where i,j=1,..,n

Many thanks for any help

Hi

I would like to compute the limit as t goes to infinity.

Let delta be a given positive real number

restart;
assume(t, positive);

g := (t,delta) arrow  maximization(minimization(abs(x^(2^(-t))-y), y = 0 .. delta), x = 0 .. 1) ;

then I would like to compute the limit of g(t,delta) as t goes to infinity

Many thanks for any help

Hi

I would like to compute the limit as t goes to +infinity of

restart;
assume(t, positive);

g(t):=minimize(abs(x^(2^(-t))-1),x=1-delta.1+delta);

where delta is very small such that 1- delta is positive.

Then I would like to compute the limit as to goes to infinity of g(t)

Many thanks

Hi,

I need your help to classify the follwing set {0}, {1} and [0,1] are local attractor or not and in the case of local attractor how can we determine the bassin of attraction. 

ode:=diff(x(t),t)=sqrt(x(t));

how can we prove using maple which of {0}, {1} and [0,1] are local attarctor or not.

Many thanks

Hi

I have the ODEs: x'=x

ode:=diff(x(t),t)-x(t);

sketch the phase space and extended phase space of previous ode.