A new Jacobi spectral collocation method for solving 1+1 fractional Schrodinger equations and fractional coupled Schrodinger systems
Abbreviated Journal Title
Eur. Phys. J. Plus
PARTIAL-DIFFERENTIAL-EQUATIONS; DISCONTINUOUS GALERKIN METHOD; QUANTUM-MECHANICS; INTEGRODIFFERENTIAL EQUATIONS; VARIABLE-COEFFICIENTS; DIFFUSION-EQUATIONS; OPERATIONAL MATRIX; NUMERICAL-SOLUTION; TAU METHOD; ORDER; Physics, Multidisciplinary
The Jacobi spectral collocation method (JSCM) is constructed and used in combination with the operational matrix of fractional derivatives (described in the Caputo sense) for the numerical solution of the time-fractional Schrodinger equation (T-FSE) and the space-fractional Schrodinger equation (S-FSE). The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations, which greatly simplifies the solution process. In addition, the presented approach is also applied to solve the time-fractional coupled Schrodinger system (T-FCSS). In order to demonstrate the validity and accuracy of the numerical scheme proposed, several numerical examples with their approximate solutions are presented with comparisons between our numerical results and those obtained by other methods.
European Physical Journal Plus
"A new Jacobi spectral collocation method for solving 1+1 fractional Schrodinger equations and fractional coupled Schrodinger systems" (2014). Faculty Bibliography 2010s. 5076.