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MULTICOMPLEX TAYLOR SERIES EXPANSION FOR COMPUTING HIGH-ORDER DERIVATIVES

H.R. Millwater, S. Shirinkam
2014 International Journal of Applied Mathematics  

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Multicomplex Taylor series expansion (MCTSE) is a numerical method for calculating higher-order partial derivatives of a multivariable realvalued and complex-valued analytic function based on Taylor series expansion without subtraction cancelation errors. The implementation has been facilitated using Cauchy-Riemann matrix representation of multicomplex variables. In this paper, we show steps for finding these matrices and, in addition, that the number of appearances of the k th derivatives
more » ... ws the Pascal's triangle. Also, the situations where the MCTSE is not applicable is determined. Finally, we investigate the application of the method for complex-valued functions.
doi:10.12732/ijam.v27i4.2 fatcat:wdxna3osgrgffcwgjytlbxjtpi
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H.R. Millwater, S. Shirinkam. "MULTICOMPLEX TAYLOR SERIES EXPANSION FOR COMPUTING HIGH-ORDER DERIVATIVES." International Journal of Applied Mathematics 27.4 (2014)