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\textbf{FlexBox} is a flexible MATLAB toolbox for finite dimensional convex variational problems in image processing and beyond. Such problems often consist of non-differentiable parts and involve linear operators. The toolbox uses a…

We present an improved version of our program package oneloop which -- written as a package for MAPLE -- solves one-loop Feynman integrals. The package is calculating one-, two- and three-point functions both algebraically and numerically…

Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…

This paper introduces a new computational framework to derive electromagnetic field derivatives with respect to multiple design parameters up to any order with the Finite-Difference Time-Domain (FDTD) technique. Specifically, only one FDTD…

We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness…

In this paper, we introduce two new non-singular kernel fractional derivatives and present a class of other fractional derivatives derived from the new formulations. We present some important results of uniformly convergent sequences of…

Many uncertainty propagation software exist, written in different programming languages, but not all of them are able to handle functional correlation between quantities. In this paper we review one strategy to deal with uncertainty…

The use of neural networks for solving differential equations is practically difficult due to the exponentially increasing runtime of autodifferentiation when computing high-order derivatives. We propose $n$-TangentProp, the natural…

We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational…

Higher order derivatives of functions are structured high dimensional objects which lend themselves to many alternative representations, with the most popular being multi-index, matrix and tensor representations. The choice between them…

Implementing and executing numerical algorithms to solve fractional differential equations has been less straightforward than using their integer-order counterparts, posing challenges for practitioners who wish to incorporate fractional…

Recently, the authors Khalil, R., Al Horani, M., Yousef. A. and Sababheh, M., in " A new Denition Of Fractional Derivative, J. Comput. Appl. Math. 264. pp. 6570, 2014. " introduced a new simple well-behaved definition of the fractional…

We address the task of higher-order derivative evaluation of computer programs that contain QR decompositions and real symmetric eigenvalue decompositions. The approach is a combination of univariate Taylor polynomial arithmetic and matrix…

We present a new package for Mathematica system, called Libra. Its purpose is to provide convenient tools for the transformation of the first-order differential systems $\partial_i \boldsymbol j = M_i \boldsymbol j$ for one or several…

We extend JAX with the capability to automatically differentiate higher-order functions (functionals and operators). By representing functions as a generalization of arrays, we seamlessly use JAX's existing primitive system to implement…

Differentiable programming allows for derivatives of functions implemented via computer code to be calculated automatically. These derivatives are calculated using automatic differentiation (AD). This thesis explores two applications of…

We introduce a 'grading switching' for arbitrary nonassociative algebras of prime characteristic p, aimed at producing a new grading of an algebra from a given one. We take inspiration from a fundamental tool in the classification theory of…

Undisputedly, derivation of theoretical systematic uncertainties is an inseparable ingredient of any robust analysis dealing with experimental data. However, it is not uncommon, even for those analyses that use state of the art methods and…

This short note provides an explicit description of the Fr\'echet derivatives of the principal square root matrix functional at any order. We present an original formulation that allows to compute sequentially the Fr\'echet derivatives of…

Automatic differentiation is a tool for numerically calculating derivatives of a given function up to machine precision. This tool is useful for quantum chemistry methods, which require the calculation of gradients either for the…