Hopscotch, a fast finite difference technique, is used to solve parabolic and elliptic equations in two space dimensions with a mixed derivative. The method is compared numerically with existing alternating direction implicit (A.D.I.) and locally one dimensional (L.O.D.) methods for simple problems. Douglas and Gunn's A.D.I. method is both simplified and improved by reformulating it as a hopscotch method. © 1977, All rights reserved.