The system of diffusion equations generated by SINDA is solved by an eigenmethod. This avoids the current numerical integration and its instability problems. The nonlinear terms such as radiative coupling are treated as forcing functions, and their rates of change determine the time steps, which are automatically set to yield any desired accuracy. The method can be significantly faster than the current methods.An example problem is solved in sufficient detail to allow a programmer to install the method in SINDA, so that its use would be just as convenient as calling for the Crank-Nicholson method. Existing SINDA models could be run without change, and the modelling advantages of SINDA are retained.