Application of binomial coefficients in representing central difference solution to a class of PDE arising in chemistry

摘要

The use of differential equations for modeling chemical systems and solving by numerical approaches (e.g. finite difference methods) are prevalent in chemistry-related problems. As an extension to the direct use of Pascal's Triangle to obtain the forward and backward difference equations to partial differentials by Lim [Mathematical Medley 31 (2004) 2], this paper proposes the use of binomial coefficient to generate central difference equations to odd-ordered partial differentials in a single-step operation. All finite difference equations to partial differentials shown herein display finite series of palindromic coefficients with alternating signs.