SIAM Undergraduate Research Online
Volume 15
In This Volume
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Numerical Computation of Fractional Derivatives of Complex-Valued Analytic Functions
Published electronically December 27, 2022DOI: 10.1137/22S1520566
Authors
Austin Higgins (Michigan Technological University)
Project Advisors
Cecile Piret (Michigan Technological University) and Bengt Fornberg (University of Colorado)
Abstract
Highly accurate numerical approximations of analytic Caputo fractional derivatives are difficult to compute due to the upper bound singularity in its integral definition. However, it has been recently demonstrated that Caputo fractional derivatives of analytic functions can be numerically evaluated to double-precision accuracy by utilizing only function values in a grid. This is done by considering a modified Trapezoidal Rule (TR) and placing equispaced finite difference (FD) correction stencils at both endpoints. In terms of complex-valued analytic functions f(z), these fractional derivatives are multi-valued. In this paper, we provide several test functions for this numerical method of evaluating Caputo fractional derivatives. We produce figures of the principal branch of the functions’ approximated fractional derivatives, and include error plots of these approximations.
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hp Gauss-Legendre Quadrature for Layer Functions
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The Effects of Seasonality on Competition for a Limiting Resource
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COVID-19, Crowdedness, and CMC Dining: An Agent-Based Model Approach to Reducing the Spread of COVID-19
Published electronically December 7, 2022 -
The Effect of Academic Performance on Athletic Success in Collegiate Athletic Programs
Published electronically November 28, 2022 -
Characterising Dark Matter Substructure in Gravitational Lens Galaxies with Deep Learning
Published electronically October 28, 2022 -
A Probabilistic Analysis of Shotgun Sequencing for Metagenomics
Published electronically October 14, 2022 -
Quantum Evolution in One Dimensional Disordered Systems: Localisation and Oscillations
Published electronically October 13, 2022 -
Accelerating Parameter Inference in Diffusion-Reaction Models of Glioblastoma Using Physics-Informed Neural Networks
Published electronically October 11, 2022 -
Rapid Testing in COVID and Modified SIR Model
Published electronically October 4, 2022 -
An Agent-Based Model of COVID-19 on the Diamond Princess Cruise Ship
Published electronically September 29, 2022 -
Analysis of Legal Documents via Non-negative Matrix Factorization Methods
Published electronically September 27, 2022 -
Discretized Migration Flow: A Vector Field Based Tool for Avian Mobility in Patchy Mechanistic Models of Early Pathogenic Spread
Published electronically September 20, 2022 -
A Mathematical Analysis of Reconstruction Artifacts in Radar Limited Data Tomography
Published electronically September 7, 2022 -
A Tensor SVD-based Classification Algorithm Applied to fMRI Data
Published electronically August 29, 2022 -
A Numerical Study on Sparse Learning of Interaction Laws in Homogeneous Multiparticle Systems
Published electronically August 5, 2022 -
Forecasting COVID-19 Vaccine Distribution in the United States, Japan, Taiwan, and China Using the Auto-Regressive Integrated Moving Average (ARIMA) Model
Published electronically August 2, 2022 -
Neural Network Approach to NFL Position Classification
Published electronically July 28, 2022 -
Using Artificial Neural Networks to Classify Optimal Microswimmers Based on Their Shapes
Published electronically July 28, 2022 -
Statistical Learning for Best Practices in Tattoo Removal
Published electronically July 18, 2022 -
Remote Work: Fad or Future
Published electronically June 16, 2022 -
Comparison of Atlas-Based and Neural-Network-Based Semantic Segmentation for DENSE MRI Images
Published electronically May 26, 2022 -
On Application of Block Kaczmarz Methods in Low-Rank Matrix Factorization
Published electronically April 28, 2022 -
Accelerated Alternating Minimization for X-ray Tomographic Reconstruction
Published electronically April 27, 2022 -
A Numerical Investigation of Rayleigh-Benard Convection with an Obstruction
Published electronically April 1, 2022 -
Alternating Minimization for Computed Tomography with Unknown Geometry Parameters
Published electronically April 1, 2022 -
Spectral Touching Points in Two-Dimensional Materials
Published electronically February 17, 2022 -
Finding the Optimum Times to Flip a Beefsteak Using a Genetic Algorithm
Published electronically February 2, 2022 -
Clustering COVID-19 Lung Scans
Published electronically January 24, 2022
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