Higher accuracy order in differentiation-by-integration

• Main Author: Andrej Liptaj
• Format: Article
• Language: English
• Published: Vilnius Gediminas Technical University 2021-05-01
• Series: Mathematical Modelling and Analysis
• Subjects: differentiation by integration; generalized Lanczos derivative; numerical differentiation; higher-order method; accuracy
• Online Access: https://journals.vgtu.lt/index.php/MMA/article/view/13119

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 an arbitrary precision for an 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 the usual Legendre-polynomial kernels. Presented results may have implications for numerical implementations of the differentiation-by-integration method.