  We develop time-splitting finite difference methods, using implicit
Backward-Euler and semi-implicit Crank-Nicolson discretization schemes, to
study the spin-orbit coupled spinor Bose Einstein condensates with coherent
coupling in quasi-one and quasi-two-dimensional traps. The split equations
involving kinetic energy and spin-orbit coupling operators are solved using
either time-implicit Backward-Euler or semi-implicit Crank-Nicolson methods. We
explicitly develop the method for pseudospin-1/2, spin-1, and spin-2
condensates. The results for ground states obtained with time-splitting
Backward-Euler and Crank-Nicolson methods are in excellent agreement with
time-splitting Fourier spectral method which is one of the popular methods to
solve the mean-field models for spin-orbit coupled spinor condensates. We
confirm the emergence of different phases in spin-orbit coupled pseudospin-1/2,
spin-1, and spin-2 condensates with coherent coupling.
