Numerical Simulation for Fractional-Order Bloch Equation Arising in Nuclear Magnetic Resonance by Using the Jacobi Polynomials
Numerical Simulation for Fractional-Order Bloch Equation Arising in Nuclear Magnetic Resonance by Using the Jacobi Polynomials
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DOI：
10.3390/app10082850
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发表时间：
2020-02-01
影响因子：
2.7
通讯作者：
Srivastava, H. M.
中科院分区：
文献类型：
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作者：
Singh, Harendra;Srivastava, H. M.
本文利用雅可比多项式对Bloch方程的分数阶模型进行了数值模拟。它出现在化学、物理和核磁共振(核磁共振)中。它也出现在磁共振成像(MRI)和电子自旋共振(ESR)中。只要已知化合物的相对分子质量和结构，它就可用于纯度测定。它还可用于结构测定。通过对核磁共振的研究，化学家可以确定许多化合物的结构。将得到的数值结果与已知解进行了比较和模拟。给出了绝对误差和均方根误差表，说明了该方法的准确性。用图形说明了时间分数阶导数结果的不同阶次。
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.