Systolic arrays for group explicit methods for solving parabolic partial differential equations

A systolic array implementation for solving parabolic equations numerically is presented. The finite-difference methods used are stable asymmetric approximations to the partial differential equations, which when coupled in groups of two adjacent points on the grid result in implicit equations that are easily converted to explicit form, thus offering many advantages suitable for solution by VLSI techniques. The regularity obtained from the grid structure and locality of data from groups of small size, combined with the attributes of truncation error cancellations and alternating the strategies of grid points, give unconditional stability and an efficient, systolic design.<>