Related papers: Iteration scheme for initial value problem for PDE…
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
In this paper, we reconsider two new iterative methods for solving absolute value equations (AVE), which is proposed by Ali and Pan (Jpn. J. Ind. Appl. Math. 40: 303--314, 2023). Convergence results of the two iterative schemes and new…
We compute the rate of convergence of forward, backward and central finite difference $\theta$-schemes for linear PDEs with an arbitrary odd order spatial derivative term. We prove convergence of the first or second order for smooth and…
This paper focuses on proposing a deep learning initialized iterative method (Int-Deep) for low-dimensional nonlinear partial differential equations (PDEs). The corresponding framework consists of two phases. In the first phase, an…
Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical approximation.…
For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit…
In this article we introduce a simple straightforward and powerful method involving symbolic manipulation, Picard iteration, and auxiliary variables for approximating solutions of partial differential boundary value problems. The method is…
For initial value problems associated with operator-valued Riccati differential equations posed in the space of Hilbert--Schmidt operators existence of solutions is studied. An existence result known for algebraic Riccati equations is…
We examine initial-boundary value problems for diffusion equations with distributed order time-fractional derivatives. We prove existence and uniqueness results for the weak solution to these systems, together with its continuous dependency…
We perform a systematic comparison of various numerical schemes for the approximation of interface problems. We consider unfitted approaches in view of their application to possibly moving configurations. Particular attention is paid to the…
In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations…
In this note we consider the continuous Galerkin time stepping method of arbitrary order as a possible discretization scheme of nonlinear initial value problems. In addition, we develop and generalize a well known existing result for the…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
We propose new machine learning schemes for solving high dimensional nonlinear partial differential equations (PDEs). Relying on the classical backward stochastic differential equation (BSDE) representation of PDEs, our algorithms estimate…
This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest…
This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness…
In this paper we discuss a framework for the polynomial approximation to the solution of initial value problems for differential equations. The framework, initially devised for the approximation of ordinary differential equations, is…
This paper presents an iterative scheme that converges to the solution of a pseudo-monotone variational inequality problem in the setting of $\mathbb{R}^{n}$. Traditional methods often require projections onto the feasible set…