Related papers: Evaluation of the Efficiency and Comparison of Dif…

In the context of the analysis of measured data, one is often faced with the task to differentiate data numerically. Typically, this occurs when measured data are concerned or data are evaluated numerically during the evolution of partial…

The goal of this paper is to investigate an approach for derivative-free optimization that has not received sufficient attention in the literature and is yet one of the simplest to implement and parallelize. It consists of computing…

Differentiation is a cornerstone of computing and data analysis in every discipline of science and engineering. Indeed, most fundamental physics laws are expressed as relationships between derivatives in space and time. However, derivatives…

Curve fitting is a fundamental technique in engineering and scientific research, serving as a critical tool for extracting insights from data. This study explores the application of various statistical equations to estimate outcomes in…

Backward Stochastic Differential Equations (BSDEs) have been widely employed in various areas of social and natural sciences, such as the pricing and hedging of financial derivatives, stochastic optimal control problems, optimal stopping…

A study is conducted to evaluate four derivative estimation methods when solving a large sparse nonlinear programming problem that arises from the approximation of an optimal control problem using a direct collocation method. In particular,…

This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…

Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…

Computing derivatives of noisy measurement data is ubiquitous in the physical, engineering, and biological sciences, and it is often a critical step in developing dynamic models or designing control. Unfortunately, the mathematical…

In differential equation discovery algorithms, numerical differentiation is usually a fixed preliminary step. Current methods improve robustness with data subsampling and sparsity but often ignore the variability from the differentiation…

We derived the formulae of central differentiation for the finding of the first and second derivatives of functions given in discrete points, with the number of points being arbitrary. The obtained formulae for the derivative calculation do…

This contribution proposes a new formulation to efficiently compute directional derivatives of order one to fourth. The formulation is based on automatic differentiation implemented with dual numbers. Directional derivatives are particular…

Numerical methods: mimetic finite differences and finite elements, are analyzed from a numerical point of view. It seeks to conclude on the efficiency, order of convergence and computational cost of these methods. The analysis is done in…

This paper presents a comparative study three numerical schemes such as Linear, Quadratic and Quadratic-Linear scheme for the fractional integro-differential equations defined in terms of the Caputo fractional derivatives. The error…

We compare traditional approach of computing logarithmic returns with the fractional differencing method and its tempered extension as methods of data preparation before their usage in advanced machine learning models. Differencing…

The differentiable programming paradigm is a cornerstone of modern scientific computing. It refers to numerical methods for computing the gradient of a numerical model's output. Many scientific models are based on differential equations,…

We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files…

Computational methods for fractional differential equations exhibit essential instability. Even a minor modification of the coefficients or other entry data may switch good results to the divergent. The goal of this paper is to suggest the…

Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine…

In this paper, we consider the numerical pricing of financial derivatives using Radial Basis Function generated Finite Differences in space. Such discretization methods have the advantage of not requiring Cartesian grids. Instead, the nodes…