Unconditionally positive finite difference and standard explicit finite difference schemes for power flow equation

Power flow equation for step-index glass optical fiber was solved using recently reported unconditionally-positive finite difference (UPFD) scheme. Solution obtained using UPFD scheme was compared with solution obtained using standard explicit finite difference (EFD) scheme. For accuracy testing both schemes were compared with analytical solution for steady state distribution of given fiber. The advantage of UPFD is reflected in stability of the scheme regardless of discretization step taken. Nevertheless EFD scheme has better concurrence with analytical solution than UPFD. This is due to the additional truncation-error terms in the approximations of the first and second derivatives with respect to θ.