Analysis of operator splitting methods for the dispersive-Fisher equation

Operator splitting is a powerful method for the numerical investigation of complicated problems. The basic idea behind operator splitting methods is to split a problem into simpler sub-problems. This study focuses on analyzing the convergence of operator splitting methods applied to the dispersive-Fisher equation. The equation is initially split into unbounded linear and bounded nonlinear components. Operator splitting techniques of the Lie-Trotter and Strang types are then applied to the equation. Local error bounds are derived using an approach based on the differential theory of operators in Banach space and the error terms of one- and two-dimensional numerical quadratures using Lie commutator bounds. Global error estimates are derived using Lady Windermere's fan argument. Finally, a numerical example is examined to confirm the expected rate of convergence.