IMPLEMENTATION OF GENERALIZED FINITE-DIFFERENCE FORMULAS AND TRUNCATION ERRORS FOR EACH DERIVATIVE

Through Taylor series expansion, a generalized formulation which can s how any finite difference expression along with its truncation error f or each derivative has been introduced in the present study. Thereafte r, several well-known finite difference and finite element formulas fo r the first and second derivatives are demonstrated to compare with th eir truncation errors. As to the applications, higher-order terms of t runcation error can be incorporated into finite difference equation to get more accurate results. In addition, a new scheme is proposed to g enerate an optimum finite difference equation where its total truncati on error is minimized.