Eugene Stephane Mananga
The City University of New York, USA
Numerical methods for differential equations are one of the notable glories of contemporary science. Coupled with much algorithmic ingenuity, numerical methods are widely applied across science and engineering fields. One of the most important numerical methods is the numerical integration which has been the focus of intense research since its development in 1915 by David Gibb. In this abstract, we present the study of numerical integrator based on Fer expansion in the integration of the time-dependent Schrodinger equation (TDSE) which is a central problem to nuclear magnetic resonance (NMR) in general and solid-state NMR in particular. Numerical simulations of NMR experiments are often required for the development of new techniques and for the extraction of structural and dynamic information from the spectra. The development and design of various pulse sequences and understanding of different NMR experiments are based on the form of effective Hamiltonian or effective propagator that satisfies the TDSE which is difficult to solve unless the Hamiltonian is time independent or commutes with itself at two different times. The evolution operator allows obtaining the density matrix of the spin system that has evolved from the equilibrium density matrix due to the application of RF irradiation. The signal intensity depends on the final density matrix of the spin system. For example, if the numerical model is implemented with the approximate solutions of Fer or Magnus, the results of the simulation will show incorrect or undesirable effects of finite pulses and ring-down mainly when dealing with quadrupolar nuclei (I>1/2). In this study we proposed an efficient numerical integrator based on Fer expansion for solving the TDSE to obtain an effective propagator that continually improves the detected NMR signal. We will also compare the performance of the numerical integrator based on Fer expansion with respect to other Lie-group solvers, namely Magnus and Cayley methods.