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In this text explicit forms of several higher precision order kernel functions (to be used in the differentiation-by-integration procedure) are given for several derivative orders. Also, a system of linear equations is formulated which allows to construct kernels with arbitrary precision for arbitrary derivative order. A computer study is realized and it is shown that numerical differentiation based on higher precision order kernels performs much better (w.r.t. errors) than the same procedure based on usual Legendre-polynomial kernels. Presented results may have implications for numerical implementations of the differentiation-by-integration method.

HIGHER ACCURACY ORDER IN DIFFERENTIATION-BY-INTEGRATION