Minimization of Computational Errors in 1D Diffusion Simulation of Nuclear Magnetization

The finite-difference method is used for solving the diffusion equation of nuclear magnetization in discrete space and time. The purpose of this study was to obtain the time step Deltat and the spatial step Deltax, which minimize computational errors in simulation. We evaluated the difference between a discrete solution and an explicit solution that had been derived from the magnetization diffusion equation. The results revealed the existence of Deltax, which minimizes computational errors. The spatial step Deltax and computational errors increased as the time step Deltat increased. The results should be useful for efficiently carrying out diffusion simulations within given time limitations for computation.