Related papers: A fitted scheme for a Caputo initial-boundary valu…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
This paper presents a numerical method to solve a time-fractional Burgers equation, achieving order of convergence $(2-\alpha)$ in time, here $\alpha$ represents the order of the time derivative. The fractional derivative is modeled by…
In this research work, we propose a high-order time adapted scheme for pricing a coupled system of fixed-free boundary constant elasticity of variance (CEV) model on both equidistant and locally refined space-grid. The performance of our…
Isoperimetric problems consist in minimizing or maximizing a cost functional subject to an integral constraint. In this work, we present two fractional isoperimetric problems where the Lagrangian depends on a combined Caputo derivative of…
We consider a space-time fractional parabolic problem. Combining a sinc-quadrature based method for discretizing the Riesz-Dunford integral with $hp$-FEM in space yields an exponentially convergent scheme for the initial boundary value…
We consider time-fractional parabolic equations with a Caputo time derivative of order $\alpha\in(0,1)$. For such equations, we give an elementary proof of the weak maximum principle under no assumptions on the sign of the reaction…
Solving initial value problems and boundary value problems of Linear Ordinary Differential Equations (ODEs) plays an important role in many applications. There are various numerical methods and solvers to obtain approximate solutions…
In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large…
A nonlinear Helmholtz (NLH) equation with high frequencies and corner singularities is discretized by the linear finite element method (FEM). After deriving some wave-number-explicit stability estimates and the singularity decomposition for…
This article deals with the numerical analysis of the Cauchy problem for the Korteweg-de Vries equation with a finite difference scheme. We consider the Rusanov scheme for the hyperbolic flux term and a 4-points $\theta$-scheme for the…
In this paper, we propose a novel numerical scheme for solving time-fractional reaction-diffusion problems with Robin boundary conditions, where the time derivative is in the Caputo sense of order $\alpha\in(0,1)$. The existence and…
This paper is concerned with monotone (time-explicit) finite difference schemes associated with first order Hamilton-Jacobi equations posed on a junction. They extend the schemes recently introduced by Costeseque, Lebacque and Monneau…
In the current work we build a difference analog of the Caputo fractional derivative with generalized memory kernel ($_\lambda$L2-1$_\sigma$ formula). The fundamental features of this difference operator are studied and on its ground some…
This study investigates a class of initial-boundary value problems pertaining to the time-fractional mixed sub-diffusion and diffusion-wave equation (SDDWE). To facilitate the development of a numerical method and analysis, the original…
A first-order linear fully discrete scheme is studied for the incompressible time-dependent Navier-Stokes equations in three-dimensional domains. This scheme, based on an incremental pressure projection method, decouples each component of…
This paper presents the error analysis of numerical methods on graded meshes for stochastic Volterra equations with weakly singular kernels. We first prove a novel regularity estimate for the exact solution via analyzing the associated…
A unified framework to derive optimized compact schemes for a uniform grid is presented. The optimal scheme coefficients are determined analytically by solving an optimization problem to minimize the spectral error subject to equality…
In this paper, a linearized fully discrete scheme is proposed to solve the two-dimensional nonlinear time fractional Schr\"odinger equation with weakly singular solutions, which is constructed by using L1 scheme for Caputo fractional…
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…
Based on our recent results, in this paper, a compact finite difference scheme is derived for a time fractional differential equation subject to the Neumann boundary conditions. The proposed scheme is second order accurate in time and…