C++ :: Finite Difference Method For Partial Differential Equations?

Calculated by the explicit scheme. Produces some very large numbers.

task:

[math] U_t = 3 (1,1-0,5 x) U_ {xx} + e ^ t-1 [/ math]
[math] U (0, t) = 0 [/ math]
[math] U (1, t) = 0 [/ math]
[math] U (x, 0) = 0.01 (1-x) x [/ math]

Need to find a solution with accuracy [math] 0.0001 [/ math] on the interval [math] T = 1 / a ^ *, where a ^ * = max a (x, t) [/ math] Plot graphs of functions [math] u (x ^ *, t), u (x, jt ^ *) [/ math] where [math] x ^ * = 0.6, t ^ * = T/10, j = 1,2,4 [/ math]

explicit difference scheme is as follows:

([math] $ u_t ^ {j +1}-u_i ^ j) / tau = 3 (1,1-0,5 x_i) (u_ {i +1} ^ {j}-2u_i ^ j + u_ {i -1} ^ j) / h ^ 2 + e ^ {t_j} +1 $ $ [/ math]

code of the program:

int main ( void ) {
setlocale(LC_ALL, "rus");
int I = 10, J = 30, i, j;
double T = 1.0/ pow(3.3, 0.5), h_x = 1.0/ I, h_t = T/ J, epsilon = h_t + pow(h_x, 2), c;
double **u = new double *[I + 1];
for (i = 0; i <= I; i++) u[i] = new double [J + 1];

[code]....

displays the following:

[URL]