Nonlinear systems with periodic variations of nonlinearity and/or dispersion occur in a
variety of physical problems and engineering applications. The mathematical concept of …

We develop a class of numerical methods for stiff systems, based on the method of
exponential time differencing. We describe schemes with second-and higher-order …

A modification of the exponential time-differencing fourth-order Runge--Kutta method for
solving stiff nonlinear PDEs is presented that solves the problem of numerical instability in …

We study the numerical solution of the time-dependent Gross–Pitaevskii equation (GPE)
describing a Bose–Einstein condensate (BEC) at zero or very low temperature. In …

We studied the efficiency of different implementations of the split-step Fourier method for
solving the nonlinear Schrödinger equation that employ different step-size selection criteria …

The integrating factor (IF) method for numerical integration of stiff nonlinear PDEs has the
disadvantage of producing large error coefficients when the linear term has large norm. We …

Many chemical systems exhibit a range of patterns, a noticeable and interesting class of
numerical patterns that arise in autocatalytic reactions which changes with increasing spatial …

Split-step procedures have previously been used successfully in a number of situations, eg
for Hamiltonian systems, such as certain nonlinear wave equations. In this study, we note …

This paper introduces two new modified fourth-order exponential time differencing Runge–
Kutta (ETDRK) schemes in combination with a global fourth-order compact finite difference …

The generalized nonlinear Schrödinger (GNLS) equation is solved numerically by a split-
step Fourier method. The first, second and fourth-order versions of the method are …