Except in cases where an exact solution is known, partial differential equations are usually solved numerically by using a finite difference equation to replace the original equation. In this finite difference equation, the range of the independent variables, ξᵢ and t, of the differential equation is divided into the increments Δξᵢ, Δt. Courant, Friedrichs, and Lewy first observed in 1928 that it is necessary to maintain a certain "mesh ratio"-- that is, a certain ratio Δξᵢ/Δt--in order to assure convergence of the numerical solution to the exact solution. Little more was done for some fifteen years, until World War II. At that time high- speed digital computers facilitated the solution of certain partial differential equations, such as those connected with neutron diffusion.
