Related papers: Iteration scheme for initial value problem for PDE…
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…
Integral deferred correction (IDC) methods have been shown to be an efficient way to achieve arbitrary high order accuracy and possess good stability properties. In this paper, we construct high order operator splitting schemes using the…
The problem of iterated partial summations is solved for some discrete distributions defined on discrete supports. The power method, usually used as a computational approach to finding matrix eigenvalues and eigenvectors, is in some cases…
Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…
In this work, we present a result on the local existence and uniqueness of solutions to nonlinear Partial Differential-Algebraic Equations (PDAEs). By applying established theoretical results, we identify the conditions that guarantee the…
Value Iteration is a widely used algorithm for solving Markov Decision Processes (MDPs). While previous studies have extensively analyzed its convergence properties, they primarily focus on convergence with respect to the infinity norm. In…
We explore a new simulation scheme for partial differential equations (PDE's) called Information Field Dynamics (IFD). Information field dynamics attempts to improve on existing simulation schemes by incorporating Bayesian field inference,…
In this paper, we introduce an iterative numerical method to solve systems of nonlinear equations. The third-order convergence of this method is analyzed. Several examples are given to illustrate the efficiency of the proposed method.
In this paper we introduce a procedure for identifying optimal methods in parametric families of numerical schemes for initial value problems in partial differential equations. The procedure maximizes accuracy by adaptively computing…
A method for constructing first integral preserving numerical schemes for time-dependent partial differential equations on non-uniform grids is presented. The method can be used with both finite difference and partition of unity approaches,…
Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…
We extend the piecewise orthogonal collocation method to computing periodic solutions of coupled renewal and delay differential equations. Through a rigorous error analysis, we prove convergence of the relevant finite-element method and…
Through introducing a new iterative formula for divided differnce using Neville's and Aitken's algorithms,we study new iterative methods for interpolation,numerical differentiation and numerical integration formulas with arbitrary order of…
The aim of this paper is to study a whole class of first order differential inclusions, which fit into the framework of perturbed sweeping process by uniformly prox-regular sets. After obtaining well-posedness results, we propose a…
This work deals with the problem of choosing a time step for the numerical solution of boundary value problems for parabolic equations. The problem solution is derived using the fully implicit scheme, whereas a time step is selected via…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
This work is focused on the solvability of initial-boundary value problems for degenerate parabolic partial differential equations that arise in the pricing of Asian options, and on the investigation of differential and certain qualitative…
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed…
Multirate behavior of ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) is characterized by widely separated time constants in different components of the solution or different additive terms of the…
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. An energetic variational approach has been studied in a recent work [6], in which the trajectory equation is obtained, and a few first order accurate…