Sir am trying to find exact solution for pde 

pde:={diff(u(x, y), x, x)-3*(diff(u(x, y), y, y))=-16}

with boundary conditions bc := {u(-1, y) = 0, u(1, y) = 0, diff(u(x, -1), y) = u, diff(u(x, 1), y) = -u}

pdsolve(pde union bc) assuming 1>0;
but am not getting my required answer and also in boundary condition diff(u(x, -1), y) = u 

i want to have outtput of the form uy(x,-1)=u but when i excutes this i get 0=u. 

So let me know what should i do for this

Sir am trying to find exact solution for pde 

pde:={diff(u(x, y), x, x)-3*(diff(u(x, y), y, y))=-16}

with boundary conditions bc := {u(-1, y) = 0, u(1, y) = 0, diff(u(x, -1), y) = u, diff(u(x, 1), y) = -u}

pdsolve(pde union bc) assuming 1>0;
but am not getting my required answer and also in boundary condition diff(u(x, -1), y) = u 

i want to have outtput of the form uy(x,-1)=u but when i excutes this i get 0=u. 

So let me know what should i do for this

@Carl Love yeah sir what you are saying am getting it but my range is from i=1..m-1 not from 0..m.I also tried with i=0..m and i am getting same results which u are saying but when i compared my answer with analytical result they differs. I tried like this also

SOL := evalf(fsolve(Eqs1, BC, var)) instead of 

SOL := evalf(fsolve(Eqs1,var)) but this also not working

@Carl Love yeah sir what you are saying am getting it but my range is from i=1..m-1 not from 0..m.I also tried with i=0..m and i am getting same results which u are saying but when i compared my answer with analytical result they differs. I tried like this also

SOL := evalf(fsolve(Eqs1, BC, var)) instead of 

SOL := evalf(fsolve(Eqs1,var)) but this also not working

@Carl Love Yeah you are right sir I checked my code again n I was making some mistake so when I corrected it range is from 1..m-1 of I.. so sir now what to do for this range

@Carl Love Yeah you are right sir I checked my code again n I was making some mistake so when I corrected it range is from 1..m-1 of I.. so sir now what to do for this range

am attaching worksheet in which am having M=N=3 but due to u[i,j+1] in my Fd equation am getting some unknown values which i have to find in Eqs1. Please let me know what to add in code further so that i can have all unknown values on one side of equation and known on other. Thanku

hmmm.mw

@Carl Love Sir what u suggested me still doesn't worked. I am still having that problem still my boundary conditions are not be utilized2d_curent_heating_C.mw

@Carl Love Sir what u suggested me still doesn't worked. I am still having that problem still my boundary conditions are not be utilized2d_curent_heating_C.mw

@Carl Love sir am solving this code which am attaching here but now problem is with just boundary conditions. As u can see in BC equation am having values for U[0,1],U[0,2] and U[3,2] equal to zero by F1 and F2 but still when F3 and F4 varies am again getting these values in BC due to which my end solution is creating problem. In general it should be like where ever U[0,1],U[0,2] and U[3,2] comes it automaticaly should become zero but in my case its not happening. So please can u suggest me any thing for_checking.mw

@Carl Love sir am solving this code which am attaching here but now problem is with just boundary conditions. As u can see in BC equation am having values for U[0,1],U[0,2] and U[3,2] equal to zero by F1 and F2 but still when F3 and F4 varies am again getting these values in BC due to which my end solution is creating problem. In general it should be like where ever U[0,1],U[0,2] and U[3,2] comes it automaticaly should become zero but in my case its not happening. So please can u suggest me any thing for_checking.mw

FD.mw SIr please kindly check this worksheet i have tried what u suggested to me  but still am not able to manage some points like [0,4], [1,4],[2,4] and [3,4]. Please let me know now what to add so that in last matrix i can have values at all nodes..

FD.mw SIr please kindly check this worksheet i have tried what u suggested to me  but still am not able to manage some points like [0,4], [1,4],[2,4] and [3,4]. Please let me know now what to add so that in last matrix i can have values at all nodes..

thanks alot sir for correcting me but sir in end you have converted array into matrix but i need graph and table what commands should i have here. Please let me know

thanks alot sir for correcting me but sir in end you have converted array into matrix but i need graph and table what commands should i have here. Please let me know