Five‐point FTCS finite‐difference methods for heat conduction

Abstract A family of five‐point second‐order forward‐time centrred‐space (FTCS) explicit finite‐difference equations for solving the one‐dimensional heat conduction (diffusion) equation with constant coefficients and Dirichlet boundary conditions is described. Some members have stability ranges larger than that of the standard three‐point FTCS equation, others are more accurate, and some are both more accurate and more stable. Values at grid points adjacent to boundaries are computed by means of an explicit procedure with stability and accuracy matching that of the equation used at interior grid points.