The top of my function is
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using namespace std;
//using namespace itpp;
//////////////////////////////////VARIABLE DECLARATION////////////////////////////////////////////
double T = 5;
double k = 2; //determines the speed of motion, used in e^ikx
bool debug = false; //True for debugging, used mainly in glut but also gives nice console output every step of the way.
double t; //the time variable
double m = 1; //mass
double c0 = 1; //beginning speed
double xcenter = 32; //x coordinate for the center of the pressure wave
double ycenter = 64; //y coordinate for the center of the pressure wave
double sigmaXY = 5; //determines the width of the pressure wave in the x
double sigma0 = 6; //determines the sigma for the daf
double tau = 0; //time step as determined by the nyquist condition, meant to be less than nyquist
double temp; //Temp double for various calculations, resets as needed
double speed; //velocity profile
double delX = 1; //Grid spacing
double tempP[upperM]; //The values of the array for the Pk
double bar = 0.1; //This is the difference between xi and xj, yi and yj, etc. Can be tuned for more accuracy.
double ** grid;
double tMax = 10000; //This is tMax, set to something needlessly big so it runs infinitely
double framesPerSec = 60; // animation rate for screen redraws
bool running; //controls animation
double expDelT;
double * dafX;
double * dafY;

and none of those are within a method. From what I can gather, the scope of the variables is such that they can be used in any method without having to be passed. That's what I wanted to happen. Then, most of those, the ones that aren't already given a value, are initilized in the init() method which is included below.
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void init()
{ if(debug)
cout << "a" << endl;
t = 0; //resets time
double upperBound = 20; //This is the upper Range for the daf calculations
tau = (c0*c0)/(k*k*100);
grid = new double*[sizeX];
for (int asdf = 0; asdf < sizeX; ++asdf)
grid[asdf] = new double[sizeY];
//Generates your gaussian
for(int y = 0; y<sizeY; y++)
{
for(int x = 0; x<sizeX; x++)
{
grid[x][y] = 0;
}
}
expDelT = exp((tau*tau)); //this is the e^deltaT^2
//Generates your DAF Kernel and stores it as an array for the X and an array for the Y
dafX = new double[sizeX];
dafY = new double[sizeY];
for(int iterDaf = 0; iterDaf<sizeX; iterDaf++)
{
dafX[iterDaf] = deltaX(upperBound, iterDaf);
}
for(int iterDaf = 0; iterDaf<sizeY; iterDaf++)
{
dafX[iterDaf] = deltaY(upperBound, iterDaf);
}
//Does all the clearing that is needed
cout << "done finally" << endl;
glClearColor(1.0, 1.0, 1.0, 0.0);//Define our background color
gluOrtho2D(0,sizeY,0,sizeX);//(NEW) Define our viewing area
glDisable(GL_DEPTH_TEST);
glEnable(GL_POINT_SMOOTH);
glPointSize(5);
//Generates your gaussian
t = 0;
for(int y = 0; y<sizeY; y++)
{
for(int x = 0; x<sizeX; x++)
{
grid[x][y] = exp((((xxcenter)*(xxcenter))/(2*sigmaXY*sigmaXY)+((yycenter)*(yycenter))/(2*sigmaXY*sigmaXY)));
}
}
}

After this, I believe that the global tau is defined as (c0*c0)/(k*k*100) and the variable t is set to zero. I did this with the intention that when you press enter in the GLUT window, it resets the whole thing.
The problem is, that in the method timestep(); which I included above, time for some reason turns into NaN. I am not sure why.
I hope that helps for clarification.
I also have a question, if I have a variable defined globally, then would I need to declare it in every method that I use it anyways?