Differentiation by Central Finite Differences

The relationships between central difference operators and differential operators, which are summarized in Table 3.3, will be used in the following sections to develop a set of formulas expressing the derivatives in terms of central finite differences. These formulas will have higher accuracy than those developed in the previous two sections using backward and forward finite differences. 

1 First-Order Derivative in Terms of Centrai Finite Differences with Error of Order 

Truncate the series, retaining only the first term  

Express the differential and averaged central difference operators in terms of Iheir respective definitions  

50) enables us to evaluate the first-order derivative of y at position i in terms of central finite differences. Comparing this equation with Eq. (4.16) and Eq. (4.33) reveals that use of central differences increases the accuracy of the formulas, for the same number of terms retained. 

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