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 calculatorfor computing differentiations numerically. These limitations are the value of D(0,O) keyed in by users using 3-point centraldifference formula, and the fact that the previous spreadsheet calculator can only calculate the approximate definitedifferentiation up to level 4 x 4. If the function to be differentiated is complicated, calculating D(0,O) using 3-point centraldifference 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 spreadsheetcalculator, we redesigned the Richardson's extrapoIation spreadsheet calculator, where users are only required to give thevalue of x, the function to be differentiated f(x), and the step size h value without writing the command to obtain D(0,O).Consequently, the calculations will be done automatically to approximate the definite differentiation up to level 10 x 10.