@Carl Love I was confused i thought Robert Lopez was suggesting me to try for searching help not for Try command. my bad.

Thanks

@Carl Love This is what i was searching from the beginning. This solved my present problem compltely.

Thanks.

@vv 

NULL means there is no solution and it is same as false. I checked and with no avail.

Thanks

@rlopez 

I was searching in help and i couldn't get any reference.

@Carl Love 

Thanks carl.That solved this problem. Out of curiosity i want to know what if in a particular program we have to get an out come if an error arises.

@Axel Vogt 

Thanks Axel I got what i need to learn. I thank you for your very fast and crisp replies.

Viel Glück.

@Axel Vogt 

I tried all three procedures and got the value with reasonable degree of accuracy. I have a doubt though is the maple internally using an interpolation function on the operands to get a polynomial and as we integrate it we get a solution.

Please can you explain.

Thanks again.

@Preben Alsholm 

Thanks preben case 1 of the boundary conditions did solve my problem.

also why do t> hfloat(0.0), matrix is singular error comes. i want to know why an error comes in our program, ofcourse of incorrect conditions. what i mean is can we have a list of all errors possible in maple and what are the possible reasons for them.

Hi guys i identified the problem in the boundary conditions

These are my final boundary conditions

k :=21.37595739:
c :=1.760652758:

v(x,t):=(u(x,t)+k*(u(x,t))^(2)):

                                    
PDE := diff(u(x, t), t)-(diff(v(x, t), x, x)) = 0:

IBC := {u(1, t) = 1, u(x, 0) = 0, (D[1](v))(0, t) = 0, (D[1](v))(1, t) = c};

#but the following error is displayed in pdsolve

S := pdsolve(PDE, IBC, numeric, time = t, range = .1 .. 1);

Error, (in pdsolve/numeric/process_PDEs) number of dependent variables and number of PDE must be the same

Hi guys thanks for your replies.

I am sorry that I didn't give description to my problem. I am basically solving a diffusion induced stress under coupled conditions i.e diffusion not only influences stress but stress also influences diffusion in return and hence the non linear partial differntial equation.

My underlying equations are correct and the boundary conditions are 2 + 1 initial condition. If k=0 then the equation reduces to standard diffusion equation for a plane sheet with constant flux at one end and 0 flux at other.

I k=21.37595739 this is the case of coupled stress and diffusion problem. In both coupled and uncoupled cases there is no change in boundary and initial conditions I did not mention another boundary condtion.

These are my complete boundary conditions.

k :=21.37595739:
c :=1.760652758:

PDE := diff(u(x, t), t)-(diff(u(x, t)+k*u(x, t)^2, x, x)) = 0;
IBC := {u(1, t) = 1, u(x, 0) = 0, (D[1](u))(0, t) = 0, (D[1](u))(1, t) = c};
S := pdsolve(PDE, IBC, numeric, time = t, range = .1 .. 1);
Es := 0.117108e12;
Ef := 0.78125e11;
l := 0.150e-6;
s := 0.500000e-3;
f := 0.5898334197e-6;
o := 0.9e-5;
d := 0.10e-17;
cb := 0.1e7/(19.9);
R := 8.3144621;
T := 298;
k := 21.37595739:
c :=1.760652758:



PDE := diff(u(x, t), t)-(diff(u(x, t)+k*u(x, t)^2, x, x)) = 0;
IBC := {u(1, t) = 1, u(x, 0) = 0, (D[1](u))(0, t) = 0, (D[1](u))(1, t) = c};
S := pdsolve(PDE, IBC, numeric, time = t, range = .1 .. 1);

Error, (in pdsolve/numeric/par_hyp) values in range argument must match input boundary conditions

there is a error message in even pdsolve, hence i omiitted the boundary condition (D[1](u))(0, t) = 0.

Thanks

Mobius