Some approximateons of complex-valued functions by finite differences

In this thesis, some approximations of derivatives of complex-valued functions are described. Finite differences for first and second order derivatives of complex-valued functions are considered. In the interior points of domain, the first, second, third and fourth order of accuracy finite differences to calculate derivatives ω_z and ω_z ̅ of complex-valued function ω(z) with respect z and z ̅ are studied. Later, in the interior points of domain, finite differences to calculate approximate value of derivatives ω_zz, ω_(z ̅z) and ω_(z ̅z ̅ ) for function ω(z) are investigated. Error analyses in test examples are carried out by using Matlab program. Key Words: Finite difference, complex value, complex valued function, Approximation, Forward difference, Backward Difference, Center difference, Taylor's decomposition