Numerical Simulation for Fractional-Order Bloch Equation Arising in Nuclear Magnetic Resonance by Using the Jacobi Polynomials
Date
2020
Authors
Singh, Harendra
Srivastava, H.M.
Journal Title
Journal ISSN
Volume Title
Publisher
Applied Sciences
Abstract
n the present paper, we numerically simulate fractional-order model of the Bloch equation by using the Jacobi polynomials. It arises in chemistry, physics and nuclear magnetic resonance (NMR). It also arises in magnetic resonance imaging (MRI) and electron spin resonance (ESR). It is used for purity determination, provided that the molecular weight and structure of the compound is known. It can also be used for structural determination. By the study of NMR, chemists can determine the structure of many compounds. The obtained numerical results are compared and simulated with the known solutions. Accuracy of the proposed method is shown by providing tables for absolute errors and root mean square errors. Different orders of the time-fractional derivatives results are illustrated by using figures.
Description
Keywords
fractional-order Bloch equation, nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI), electron spin resonance (ESR), Jacobi polynomials
Citation
Singh, H. & Srivastava, H. M. (2020). Numerical simulation for fractional-order Bloch equation arising in nuclear magnetic resonance by using the Jacobi polynomials. Applied Sciences, 10(8). https://doi.org/10.3390/app10082850