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NUMERICAL DIFFERENTIATION There are two major reasons for considering numeri-
 

Summary: NUMERICAL DIFFERENTIATION
There are two major reasons for considering numeri-
cally approximations of the differentiation process.
1. Approximation of derivatives in ordinary differen-
tial equations and partial differential equations.
This is done in order to reduce the differential
equation to a form that can be solved more easily
than the original differential equation.
2. Forming the derivative of a function f(x) which is
known only as empirical data {(xi, yi) | i = 1, . . . , m}.
The data generally is known only approximately,
so that yi f(xi), i = 1, . . . , m.
Recall the definition
f0(x) = lim
h0
f(x + h) - f(x)
h
This justifies using
f0(x)
f(x + h) - f(x)

  

Source: Atkinson, Kendall - Departments of Computer Science & Mathematics, University of Iowa

 

Collections: Computer Technologies and Information Sciences