Decomposition Methods for Differential Equations

On the numerical solution of Korteweg–de Vries equation by the iterative splitting method

“…Note that this approach gives advantage since the nonlinear problem can be analyzed as a linear problem. The consistency of the method can be seen in [7].…”

“…Then each sub-equation is combined with the iterative schemes, each of which is efficiently solved with suitable integrators [5,4,8,7].…”

“…Many powerful methods have been presented, for instance, Darboux transformation method [9], Adomians decomposition method [15,11], He's perturbation method [16], Operator splitting method [10], Iterative splitting method [7].…”

An explicit Eulerian method for multiphase flow with contact line dynamics and insoluble surfactant

“…For our purposes, a productive view is given by J. Geiser, see e.g. the recent text-book [25], where the focus is, as here, the efficient and accurate treatment of complex modelling problems involving PDEs. The terminology is "decomposition methods", and aptly so: the original problem is decomposed into simpler problems and (approximate) solutions of these problems is "composed" into a consistent approximation of the original (hard) problem.…”

The Operator Splitting Method for Black-Scholes Equation

“…To overcome this drawback, in 60's or early 70's so called the decomposition methods or splitting methods have been introduced [11]. The main idea of these methods is to decouple a complex equation in various simpler equations and to solve the simpler equations with adapted discretization and solver methods.…”