This study presents, a numerical method for the solutions of the generalized nonlinear Benjamin-Bona-Mahony-Burgers' equation, with variable order local time fractional derivative. This derivative is expressed as a product of two functions, the ...

A nonlinear sea-ice problem is considered in a least-squares finite element setting. The corresponding variational formulation approximating simultaneously the stress tensor and the velocity is analyzed. Under additional smoothness assumptions, ...

In this paper, we investigate a fully discrete approximation of stochastic diffusion-wave equation driven by additive tempered fractional Gaussian noise. This additive noise exhibits semi-long range dependence. The model involves two nonlocal ...

We prove error estimates for the Raviart-Thomas interpolation in weighted L 2-norm for functions in appropriate weighted Sobolev spaces. These results allow us to obtain a priori error estimates in the fractional order case for mixed ...

Nine point sixth order compact numerical approximations are suggested to solve 2D nonlinear elliptic partial differential equations (NLEPDEs) and for the estimation of normal derivatives on a uniform rectangular grid subject to Dirichlet boundary ...

The aim of this work is to propose two efficient schemes to handle the accuracy near the singularity at t = 0 in solving two-dimensional time-fractional diffusion-wave equation (TFDWE). The considered time fractional derivative is in the Caputo ...

This work deals with a higher order numerical approximation for analyzing a class of multi-term time fractional partial integro-differential equations involving Volterra integral operators. The solutions to these problems have a mild singularity ...

We discuss the approximation of the eigensolutions associated with the Maxwell eigenvalue problem in the framework of least-squares finite elements. We write the Maxwell curl curl equation as a system of two first order equations and design a ...

A learning technique for finite horizon optimal control problems and its approximation based on polynomials is analyzed. It allows to circumvent, in part, the curse dimensionality which is involved when the feedback law is constructed by using ...

In this paper, we mainly study two spectral Galerkin approximation schemes of the FitzHugh-Nagumo (FHN) neuron model for the nerve impulse propagation, which contains a small parameter perturbation and strong nonlinearity. To this end, we ...

In this paper, we use direct meshless local Petrov-Galerkin (DMLPG) methods for solving the variable-order time-fractional mobile/immobile advection-diffusion equation in two dimensions. The basis of the DMLPG methods is on the generalized moving ...

We introduce a filtering technique for Discontinuous Galerkin approximations of hyperbolic problems. Following an approach already proposed for the Hamilton-Jacobi equations by other authors, we aim at reducing the spurious ...

• Filtering technique for hyperbolic problems.
• Monotonization for high order DG ...

In this paper, we study the numerical approximation of the time fractional Cahn-Hilliard equation with initial singularity. A nonlinear fully discrete scheme is constructed using the L2-1 σ formula of time fractional order derivative ...

The generalized finite difference method (GFDM) is a typical meshless collocation method based on the Taylor series expansion and the moving least squares technique. In this paper, we first provide theoretical results of the meshless ...

We design a virtual element method for the numerical treatment of the two-dimensional parabolic variational inequality problem on unstructured polygonal meshes. Due to the expected low regularity of the exact solution, the virtual ...

In this paper, we develop and analyze an efficient spectral method for the transmission eigenvalue problem. By rewriting the original problem into its equivalent fourth order coupled linear eigenvalue problem, a new variational ...

We study three numerical approximations of solutions of nonlocal diffusion evolution problems which are inspired in algorithms for computing the bilateral denoising filtering of an image, and which are based on functional ...

We propose, analyze mathematically, and study numerically a novel approach for the finite element approximation of the spectrum of second-order elliptic operators. The main idea is to reduce the stiffness of the problem by subtracting ...

This paper studies the numerical solution of a two-dimensional quenching type nonlinear reaction-diffusion problem via dimensional splitting. The variable coefficient differential equation considered possesses a nonlinear forcing term, ...

In this article, a higher dimensional nonlinear boundary-value problem, viz., Gelfand-Bratu (GB) problem, is solved numerically. For the three-dimensional case, we present an accurate and efficient nonlinear multigrid (MG) approach and ...