A reliable method based on second kind Chebyshev polynomial for the fractional model of Bloch equation

Abstract

In this paper we present a reliable method based on second kind Chebyshev polynomial for the approximate solution of fractional Bloch equation in Nuclear Magnetic Resonance (NMR). The main advantages of the proposed method that it converts the fractional Bloch equation into a set of linear algebraic equations which relax the problem. Convergence and error analysis of the proposed method is given. The numerical results from suggested method and exiting methods are compared and it is observed that the results from suggested method are more accurate. Absolute errors and root mean square errors tables are given to show the accuracy of the proposed approximate method. Computational order is listed for proposed method in the form of the table. Graphs of approximate solutions are plotted by taking different time fractional derivatives. 2000 Mathematical Subject Classification: 26A33, 65L05, 65C20, Keywords: Fractional model of Bloch equation, Second kind Chebyshev polynomial, Convergence analysis, Error analysis, Liouville-Caputo fractional derivative