Hello everyone,

I am trying to solve a system of odes but it takes too much time to excute.

I have attached the sheet. Please have a look.

ode.mw

Thanks

Hello everyone,

restart:with(PDEtools):with(plots):

sys := {diff(T(x, t), t) = diff(T(x, t), x, x)+(diff(u(x, t), x))^2, diff(u(x, t), t) = diff(u(x, t), x, x)};

PDE:={diff(u(x,t),t)=diff(u(x,t),x$2),diff(T(x, t), t) = diff(T2(x,t), x)+(diff(u(x, t), x))^2,diff(T(x, t), x)=T2(x,t)};

BCs := {u(0,t)=sin(t), u(10,t)=0,T(0,t)=1, T(10,t)=0,u(x,0)=0,T(x,0)=0};

pds2 := pdsolve(PDE, BCs, numeric, spacestep=1/50);

I just want to plot T2(x,t) vs t for x=0.

Hello every one,

While plotting contours with grid size [200,200] my computer consume too much time to

execute the commond. To have an idea, the current process which I am running right now already

took 2380.22s and 68.60M and still its on.

Any suggestion to make the contour plot process faster?

Thanks

Hello every one,

I am facing problem with for loop. Please have a look.

My code is

restart;with(PDEtools):

Eq1:=diff(u(eta,t),t)=C*diff(u(eta,t),eta$2):

BCs := {u(0,t)=sin(t), u(L,t)=0}:

ICs := {u(eta,0)=0}:

L:=600:

sol:= pdsolve(Eq1,ICs union BCs,numeric,time=t,range=0..L);

for i from 0 to 600 do 

for t from 0 to 3 by 1 do

for C from 0 to 1 by 0.1 do

p0[C,t]:=sol:-value (C,t):

Hello everyone,

I want to know, how we can plot residual errors of the numerical scheme offered with dsolve command? This plot should show that the errors are in admissible range which indicates that the numerical scheme offers high accuracy.

For example, we have a bvp

dsolve({diff(y(x),x$2)-2*y(x)=0,y(0)=1.2,y(1)=0.9}, numeric,method=bvp[midrich]);

How to plot "Residual Error vs x" in this specific case?

 Thanks