Numerical Simulation for Fractional-Order Bloch Equation Arising in Nuclear Magnetic Resonance by Using the Jacobi Polynomials
In 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 purit...
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MDPI AG
2020-04-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/10/8/2850 |
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| author | Harendra Singh H. M. Srivastava |
| author_facet | Harendra Singh H. M. Srivastava |
| author_sort | Harendra Singh |
| collection | DOAJ |
| description | In 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. |
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| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T20:20:51Z |
| publishDate | 2020-04-01 |
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| spelling | doaj.art-00b3e05f08a942b8a52a4197e83c87712023-11-19T22:11:14ZengMDPI AGApplied Sciences2076-34172020-04-01108285010.3390/app10082850Numerical Simulation for Fractional-Order Bloch Equation Arising in Nuclear Magnetic Resonance by Using the Jacobi PolynomialsHarendra Singh0H. M. Srivastava1Department of Mathematics, Post-Graduate College, Ghazipur 233001, Uttar Pradesh, IndiaDepartment of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaIn 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.https://www.mdpi.com/2076-3417/10/8/2850fractional-order Bloch equationnuclear magnetic resonance (NMR)magnetic resonance imaging (MRI)electron spin resonance (ESR)Jacobi polynomials |
| spellingShingle | Harendra Singh H. M. Srivastava Numerical Simulation for Fractional-Order Bloch Equation Arising in Nuclear Magnetic Resonance by Using the Jacobi Polynomials Applied Sciences fractional-order Bloch equation nuclear magnetic resonance (NMR) magnetic resonance imaging (MRI) electron spin resonance (ESR) Jacobi polynomials |
| title | Numerical Simulation for Fractional-Order Bloch Equation Arising in Nuclear Magnetic Resonance by Using the Jacobi Polynomials |
| title_full | Numerical Simulation for Fractional-Order Bloch Equation Arising in Nuclear Magnetic Resonance by Using the Jacobi Polynomials |
| title_fullStr | Numerical Simulation for Fractional-Order Bloch Equation Arising in Nuclear Magnetic Resonance by Using the Jacobi Polynomials |
| title_full_unstemmed | Numerical Simulation for Fractional-Order Bloch Equation Arising in Nuclear Magnetic Resonance by Using the Jacobi Polynomials |
| title_short | Numerical Simulation for Fractional-Order Bloch Equation Arising in Nuclear Magnetic Resonance by Using the Jacobi Polynomials |
| title_sort | numerical simulation for fractional order bloch equation arising in nuclear magnetic resonance by using the jacobi polynomials |
| topic | fractional-order Bloch equation nuclear magnetic resonance (NMR) magnetic resonance imaging (MRI) electron spin resonance (ESR) Jacobi polynomials |
| url | https://www.mdpi.com/2076-3417/10/8/2850 |
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