This overview is devoted to splitting methods, a class of numerical integrators intended for
differential equations that can be subdivided into different problems easier to solve than the …

We introduce a numerical framework for dispersive equations embedding their underlying
resonance structure into the discretisation. This will allow us to resolve the nonlinear …

In this paper, a bilinear three-point fourth-order compact operator is applied to solve the two-
dimensional (2D) Sobolev equation with a Burgers' type nonlinearity. In order to derive a …

In this paper, we introduce a novel class of embedded exponential-type low-regularity
integrators (ELRIs) for solving the KdV equation and establish their optimal convergence …

In this paper, we propose a first-order Fourier integrator for solving the cubic nonlinear
Schrödinger equation in one dimension. The scheme is explicit and can be implemented …

In this work, high order splitting methods have been used for calculating the numerical
solutions of Burgers' equation in one space dimension with periodic, Dirichlet, Neumann …

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Abstract The Swift–Hohenberg (SH) equation has been widely used as a model for the study
of pattern formation. The SH equation is a fourth-order nonlinear partial differential equation …

In this paper, we propose an embedded low-regularity integrator (ELRI) under a new
framework for solving the modified Korteweg-de Vries (mKdV) equation under rough data …

In this paper, we establish the optimal convergence for a second-order exponential-type
integrator from Hofmanová & Schratz (2017, An exponential-type integrator for the KdV …