偏微分方程式

While I have worked on programs to infer numerical solutions to ordinary differential equations of a single variable, I have yet to complete any work involving partial differential equations. These are somewhat more complex, as the derivatives of multiple variables are involved, so solutions involve solving for more than one variable in terms the others.
My goal is to model the Lorenz attractor graphically, so I will:
1. solve the differential equations numerically via the Euler method for x, y, and z (storing the data in arrays).
2. ploy the (x,y) coordinates (i.e. projecting the (x,y,z) system onto the xy plane)
The equations are:
dx/dt = -10(x-y)
dy/dt = -xz + 28x - y
dz/dt = xy - (8/3)z
The Euler method is:
y(n+1) = y(n) + h(f(y,t))