相关论文: On the Numerical Solution of the Far Field Refract…

An error analysis of a splitting method applied to the Zakharov system is given. The numerical method is a Lie-Trotter splitting in time that is combined with a Fourier collocation in space to a fully discrete method. First-order…

Calculating dynamical diffraction patterns for X-ray topography and similar x-ray scattering-imaging techniques require the numerical integration of the Takagi-Taupin equations. This is usually performed with a simple second order finite…

We analyze a Fourier spectral Galerkin method for the fractional Camassa-Holm (fCH) equation involving a fractional Laplacian of exponent $\alpha \in [1,2]$ with periodic boundary conditions. The semi-discrete scheme preserves both mass and…

In recent study in Ref.[7] (arXiv: 2401.12525), we have introduced a method aimed at calculating the weak-field asymptotic deflection angle. This method offers an efficient computational approach that avoids the complexities of integration…

A numerical solution to the problem of wave scattering by many small particles is studied under the assumption k<<1, d>>a, where a is the size of the particles and d is the distance between the neighboring particles. Impedance boundary…

In this contribution, a wave equation with a time-dependent variable-order fractional damping term and a nonlinear source is considered. Avoiding the circumstances of expressing the nonlinear variable-order fractional wave equations via…

We introduce a new class of fractional backward orthogonal functions designed for the spectral approximation of weakly singular adjoint Volterra integral equations. These basis functions generate an approximation space that naturally…

The paper is concerned with the numerical approximation of the Intermediate Long Wave and Benjamin-Ono systems, that serve as models for the propagation of interfacial internal waves in a two-layer fluid system in particular physical…

Fractional diffusion has become a fundamental tool for the modeling of multiscale and heterogeneous phenomena. However, due to its nonlocal nature, its accurate numerical approximation is delicate. We survey our research program on the…

We present a focal surface projection to solve the narrow depth-of-field problem in projection mapping applications. We apply a phase-only spatial light modulator to realize nonuniform focusing distances, whereby the projected contents…

This article examines a new approach to solving ordinary differential equations based on Fractional-Calculus theory. Poisson and Sturm-Liouville-type problems are studied, together with different boundary conditions. Each case is analyzed…

A modified Green operator is proposed as an improvement of Fourier-based numerical schemes commonly used for computing the electrical or thermal response of heterogeneous media. Contrary to other methods, the number of iterations necessary…

This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for…

In this paper, the solution of the multi-order differential equations, by using Mellin Transform, is proposed. It is shown that the problem related to the shift of the real part of the argument of the transformed function, arising when the…

The purpose of this work is to study a finite element method for finding solutions to the eigenvalue problem for the fractional Laplacian. We prove that the discrete eigenvalue problem converges to the continuous one and we show the order…

It is well known that using high-order numerical algorithms to solve fractional differential equations leads to almost the same computational cost with low-order ones but the accuracy (or convergence order) is greatly improved, due to the…

In this note, a numerical method based on finite differences to solve a class of nonlinear advection-diffusion fractional differential equation is proposed. The fractional operator considered here is the fractional Riemann-Liouville…

A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized finite element method together with a mass lumping technique and an extra…

A numerical scheme for solving fractional initial value problems involving the Atangana-Baleanu fractional derivative is presented. Some examples for the proposed method are included, both for equations and systems of fractional initial…

An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…