A new numerical algorithm for fractional model of Bloch equation in nuclear magnetic resonance

Abstract

This paper presents a new algorithm based on operational matrix of fractional integrations for fractional Bloch equation in Nuclear Magnetic Resonance (NMR). For construction of operational matrix Legendre scaling functions are used as a basis. Using this operational matrix in the equations, we obtain approximate solutions for fractional Bloch equation. Convergence as well as error of the proposed method is given. Results are also compared with known solution. Absolute errors graph are plotted to show the accuracy of proposed new algorithm.