Related papers: On a splitting method for the Zakharov system
The objective of this work is the introduction and investigation of favourable time integration methods for the Gross--Pitaevskii equation with rotation term. Employing a reformulation in rotating Lagrangian coordinates, the equation takes…
In this paper, we will introduce a high order numerical method to solve the scattering problems with non-periodic incident fields and (locally perturbed) periodic surfaces. For the problems we are considering, the classical methods to treat…
Local Fourier analysis is a strong and well-established tool for analyzing the convergence of numerical methods for partial differential equations. The key idea of local Fourier analysis is to represent the occurring functions in terms of a…
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…
This work aims to construct an efficient and highly accurate numerical method to address the time singularity at $t=0$ involved in a class of time-fractional parabolic integro-partial differential equations in one and two dimensions. The…
This work proposes and analyzes a fully discrete numerical scheme for solving the Landau-Lifshitz-Gilbert (LLG) equation, which achieves fourth-order spatial accuracy and third-order temporal accuracy.Spatially, fourth-order accuracy is…
Variational time discretization schemes are getting of increasing importance for the accurate numerical approximation of transient phenomena. The applicability and value of mixed finite element methods (MFEM) in space for simulating…
We perform a systematic study of the accuracy of split-step Fourier transform methods for the time dependent Gross-Pitaevskii equation using symbolic calculation. Provided the most recent approximation for the wave function is always used…
This chapter presents some numerical methods to solve problems in the fractional calculus of variations and fractional optimal control. Although there are plenty of methods available in the literature, we concentrate mainly on approximating…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
The first order by time partial differential equations are used as models in applications such as fluid flow, heat transfer, solid deformation, electromagnetic waves, and others. In this paper we propose the new numerical method to solve a…
The time discretization of stochastic spectral fractional wave equation is studied by using the difference methods. Firstly, we exploit rectangle formula to get a low order time discretization, whose the strong convergence order is smaller…
In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…
We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy…
The fact that the first variation of a variational functional must vanish along an extremizer is the base of most effective solution schemes to solve problems of the calculus of variations. We generalize the method to variational problems…
Efficient time integration methods based on operator splitting are introduced for the Westervelt equation, a nonlinear damped wave equation that arises in nonlinear acoustics as mathematical model for the propagation of sound waves in high…
In this paper is described the general aspect of a numerical method for piecewise determin-istic Markov processes with boundary. Under very natural hypotheses, a crucial result about uniqueness of solution of a generalized Kolmogorov…
We develop and analyse a numerical method for the time-fractional nonlocal thermistor problem. By rigorous proofs, some error estimates in different contexts are derived, showing that the combination of the backward differentiation in time…
We present high order explicit geometric integrators to solve linear-quadratic optimal control problems and $N$-player differential games. These problems are described by a system coupled non-linear differential equations with boundary…
We consider a numerical scheme for Hamilton-Jacobi equations based on a direct discretization of the Lax-Oleinik semi-group. We prove that this method is convergent with respect to the time and space stepsizes provided the solution is…