Related papers: Error propagation in an explicit and an implicit n…
We present a numerical method for rigorous over-approximation of a reachable set of differential inclusions. The method gives high-order error bounds for single step approximations and a uniform bound on the error over the finite time…
In this paper we study the error propagation of numerical schemes for the advection equation in the case where high precision is desired. The numerical methods considered are based on the fast Fourier transform, polynomial interpolation…
Four types of global error for initial value problems are considered in a common framework. They include classical forward error analysis and shadowing error analysis together with extensions of both to rescaling of time. To determine the…
The commonly used one step methods and linear multi-step methods all have a global error that is of the same order as the local truncation error (as defined in…
We consider second order explicit and implicit two-step time-discrete schemes for wave-type equations. We derive optimal order aposteriori estimates controlling the time discretization error. Our analysis, has been motivated by the need to…
We are concerned with the convergence of spectral method for the numerical solution of the initial-boundary value problem associated to the Korteweg-de Vries-Kawahara equation (in short Kawahara equation), which is a transport equation…
This review summarizes all known results (up to this date) about methods of integration of the classical Lotka-Volterra systems with diffusion and presents a wide range of exact solutions, which are the most important from applicability…
We investigate a local modification of a variable-order fractional wave equation, which describes the propagation of diffusive wave in viscoelastic media with evolving physical property. We incorporate an equivalent formulation to prove the…
We analyze a discretization method for solving nonlinear integral equations that contain multiple integrals. These equations include integral equations with a Volterra series, instead of a single integral term, on one side of the equation.…
Based on a regularized Volterra equation, two different approaches for numerical differentiation are considered. The first approach consists of solving a regularized Volterra equation while the second approach is based on solving a…
A formula is given for the propagation of errors during matrix inversion. An explicit calculation for a 2 by 2 matrix using both the formula and a Monte Carlo calculation are compared. A prescription is given to determine when a matrix with…
In the paper we study some numerical solutions to Volterra equations which interpolate heat and wave equations. We present a scheme for construction of approximate numerical solutions for one and two spatial dimensions. Some solutions to…
When a large body of data from diverse experiments is analyzed using a theoretical model with many parameters, the standard error matrix method and the general tools for evaluating errors may become inadequate. We present an iterative…
We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…
We discuss a numerical algorithm for solving nonlinear integro-differential equations, and illustrate our findings for the particular case of Volterra type equations. The algorithm combines a perturbation approach meant to render a…
In the context of the analysis of measured data, one is often faced with the task to differentiate data numerically. Typically, this occurs when measured data are concerned or data are evaluated numerically during the evolution of partial…
The numerical method for solution of the weakly regular scalar Volterra integral equation of the 1st kind is proposed. The kernels of such equations have jump discontinuities on the continuous curves which starts at the origin. The…
The paper considers the integral Volterra equations of the first kind which are related to the inverse boundary-value heat conduction problem. The algorithms have been developed to numerically solve the respective integral equations, which…
In this paper, both semidiscrete and completely discrete finite volume element methods (FVEMs) are analyzed for approximating solutions of a class of linear hyperbolic integro- differential equations in a two-dimensional convex polygonal…
In this paper, we use Fourier analysis to study the superconvergence of the semi-discrete discontinuous Galerkin method for scalar linear advection equations in one spatial dimension. The error bounds and asymptotic errors are derived for…