Implementation of Airy function using Graphics Processing Unit (GPU)

M.D Patil,Chaitanya S Jage,Megha M Navada,V.A Vyawahare,Navin G Singhaniya,Yugesh C Keluskar

doi:10.1051/itmconf/20203203052

Abstract

Special mathematical functions are an integral part of Fractional Calculus, one of them is the Airy function. But it’s a gruelling task for the processor as well as system that is constructed around the function when it comes to evaluating the special mathematical functions on an ordinary Central Processing Unit (CPU). The Parallel processing capabilities of a Graphics processing Unit (GPU) hence is used. In this paper GPU is used to get a speedup in time required, with respect to CPU time for evaluating the Airy function on its real domain. The objective of this paper is to provide a platform for computing the special functions which will accelerate the time required for obtaining the result and thus comparing the performance of numerical solution of Airy function using CPU and GPU.

Highlights

Fractional calculus (FC) is a field of mathematics that deals with derivatives and integrals of arbitrary non-integer order
It is a topic which is around 320 years old!. The inception of this field can be attributed to a letter written to Guillaume de l’Hopital by Gottfried Leibniz in the year 1695 in which he mentions about fractional order derivatives, see [26], one can find the foundational work of Fractional calculus in the early papers of Niels Henrik Abel [27]
A rigorous comparative study of computation time required for evaluating the Airy function on NVIDIA Tesla K80 Central Processing Unit (CPU) and Graphics processing Unit (GPU) is presented

Summary

Introduction

Fractional calculus (FC) is a field of mathematics that deals with derivatives and integrals of arbitrary non-integer order. It is being used in engineering domain extensively due to its ability to model real-world systems more accurately than its integer order variant. The replacement of integer orders with fractional orders has resulted into various realistic and compact model in the field of various physical, engineering, automation, biomedical, chemical engineering according to the mention made in this book [13], The function can be called a “Special Function” only when it has the ability to be useful in some applications and satisfies certain special properties. Some commonly used special functions are Gamma, Gauss Hypergeometric, Airy, Bessel,etc [2]

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