Imran,

What are you actually trying to solve? Variable t7 contains expressions like

w[1, 2] == 0.001 w[0, 1] + 0.998 w[1, 1] + 0.001 w[2, 1]
w[9, 10001] == 0.001 w[8, 10000] + 0.998 w[9, 10000] + 0.001 w[10, 10000]

Are you really trying to solve tens of thousands of equations simultaneously?

Also, your general approach is kind of hard to follow. While you do want a Table of equations at the end to pass to Solve, you don't need to laboriously create a bunch of intermediate Tables. It might be clearer to create a function that outputs an equation, and then create a Table based on that function.

But if t7 really does look like you want it too, then I'd say you've exceeded what Solve can do. You might have to look for other Mathematica functions or change your approach.

You didn't test the result correctly. The solution is actually fine. Check the residuals (as below).

exprs = Apply[Subtract, t4, {1}];
exprs[[1 ;; 3]]

(* Out[398]= {-0.999984481326 + w[0, 1], -0.998 w[0, 1] + w[0, 2] - 
  0.002 w[1, 1], -0.998 w[0, 2] + w[0, 3] - 0.002 w[1, 2]} *)

s = Solve[t4];
s2 = Dispatch[s[[1]]];
Max[Abs[exprs /. s2]]

(* Out[405]= 2.22044604925*10^-16 *)

The largest is on the order of a machine double ULP. That's as good as it gets.

Sir , this time Mathematica is solving the system, but the answer is incorrect

v = 1; m = 10; h = 0.1; t = 0.1; k = 0.00001; jj = 10000; r = 0.001;

t = Table[w[i, 0] = Exp[(Cos[Pi*i*h] - 1)/(2 Pi*v)], {i, 0, m}] // N;

t1 = Table[w[0, j + 1] == (1 - 2 r) w[0, j] + 2 r*w[1, j], {j, 0, jj}];

t2 = Table[
   w[m, j + 1] == (1 - 2 r) w[m, j] + 2 r*w[m - 1, j], {j, 0, jj}];

t3 = Table[
   w[i, j + 1] == (1 - 2 r) w[i, j] + r*w[i + 1, j] + 
     r*w[i - 1, j], {i, 1, m - 1}, {j, 0, jj}];

t4 = Flatten[{t1, t2, t3}];

s = Solve[t4];

vv = Table[w[i, 1000], {i, 0, m}]; ss = vv /. s // Flatten

{0.985501, 0.978726, 0.959284, 0.929645, 0.893389, 0.854581, \
0.817182, 0.784618, 0.759545, 0.743798, 0.738435}

Table[-((ss[[i + 1]] - ss[[i - 1]])/ss[[i]])/h, {i, 2, 10}]

{0.267864, 0.511634, 0.70882, 0.840226, 0.891744, 0.856148, 0.734593, \
0.537418, 0.283805}