Numerical Instability of C Loop - c

Question

I am writing a piece of code to solve the LaPlacian at a boundary with charge density, in C. It uses the following loop:
chargeold[i] = charge[i];
charge[i] = -0.05*sgn(mat[i][j])*mat[i][j]*mat[i][j];
charge[i] = (1.0 - alpha)*charge[i] + alpha*chargeold[i];
mat[i][j] = (( mat[i][j-1] + di2*mat[i][j+1] ) / ( di2 + 1.0)) + 80.0*charge[i];
where the constant alpha is an under-relaxation parameter 0 < alpha < 1. This hasn't seemed to work and I think it may be to do with the numerical instability of the code - so far I have tried changing the constants, here -0.05, alpha and 80.0, and the sign in various the lines for calculating charge and mat[i][j] and get wildly different results depending on what I put: for example changing the coefficient of charge[i] on the last line by just 10.0 can cause the programme to get trapped inside a loop, diverge to infinity or -infinity, or quickly converge to 0 (which is not to be expected). This suggests to me a problem with the code I have created.
I have also tried condensing the calculation down into one line, or doing the same steps in different lines, and these also change the result wildy.
Any help on this would be appreciated. Thanks.
n.b. all data types are double
EDIT - full loop looks like:
do
{
sum_matdiff = 0;
for (i = 1; i < meshno; i++)
{
for (j = 1; j < meshno; j++)
{
if (bound[i][j] == 1) // holds boundary conditions
continue;
else
matold[i][j] = mat[i][j];
if ((i + j + count) % 2 == 1)
{
continue;
}
else if (j == (int)(0.3 * meshno))
{ // if statement to calculate at boundary
chargeold[i] = charge[i];
charge[i] = -0.05 * sgn(mat[i][j]) * mat[i][j] * mat[i][j];
charge[i] = (1.0 - alpha) * charge[i] + alpha * chargeold[i];
mat[i][j] =
((mat[i][j - 1] + di2 * mat[i][j + 1]) / (di2 + 1.0)) +
80.0 * charge[i];
if (i == 50)
{
printf("%f\n", charge[50]);
}
}
else
{ // calculates outside boundary
omega = 1.0 / (1.0 - 0.25 * omega * rho_sq);
mat[i][j] =
0.25 * (mat[i + 1][j] + mat[i - 1][j] + mat[i][j + 1] +
mat[i][j - 1] + (mat[i + 1][j] - mat[i - 1][j]) / (2 * i));
}
mat[i][j] = (1.0 - omega) * matold[i][j] + omega * mat[i][j];
sum_matdiff += fabs(1.0 - matold[i][j] / mat[i][j]);
}
}
count += 1;
av_diff = sum_matdiff / N;
}
while (av_diff > 0.01 || count < meshno * 2);