VaYu : Spectral methods for integro-differential equations - A Python library#
Version: 0.3 [Under Heavy Development]
Fractional calculus is a generalised form of the integer-order calculus. While an integer-order derivative is a local operator, a fractional derivative is a non-local operator. Furthermore, general fractional calculus is a further generalisation, which admits an arbitray (singular) kernel.
Such operators are rather cumbersome to solve, hence we introduce a new class of basis functions, namely, Jacobi Convolution Polynomails, which are suited for a large class of integro-differential operators (of convolution type). Indeed, project VaYu aims at building a bridge between theory and practice, by providing tools (python library) for numerical investigation (simulation)
Features#
Spectral (Element) Methods
Phyics-infomed Neural Networks
Fractional and Genereal Fractional Operators
Reduced Order Modeling (under development)
Also visit our ongoing, Fractional Calculus Seminars and associated YouTube channel
Citations#
Mehta, P. P. and Rozza, G (2025) Vayu : A Python library for integro-differential equations (in-preparation)
Licences#
VaYu is freely available under the GNU LESSER GENERAL PUBLIC LICENSE Version 2.1.
Funding / Acknowledgement#
Dates (MM/YYYY) |
Grant / funding details |
|---|---|
10/2023 - 10/2025 |
PNRR Digitalisation, Italy. PI: Prof. Gianluigi Rozza. |