Improved Richardson's Extrapolation Spreadsheet Calculator for Numerical Differentiation

摘要

In this paper, we have improved the limitations of our previous Richardson's extrapolation spreadsheet calculator for computing differentiations numerically. These limitations are the value of D(0,0) keyed in by users using 3-point central difference formula, and the fact that the previous spreadsheet calculator can only calculate the approximate definite differentiation up to level 4 x 4. If the function to be differentiated is complicated, calculating D(0,0) using 3-point central difference formula can be tedious as parentheses should be put in a proper order when writing the calculation command. Otherwise, the calculation command may lead to a wrong answer. In this improved Richardson's extrapolation spreadsheet calculator, we redesigned the Richardson's extrapolation spreadsheet calculator, where users are only required to give the value of x, the function to be differentiated f(x), and the step size h value without writing the command to obtain D(0,0). Consequently, the calculations will be done automatically to approximate the definite differentiation up to level 10 x 10.