Solving generalized pantograph equations by shifted orthonormal Bernstein polynomials
In this paper, we introduce Shifted Orthonormal Bernstein Polynomials (SOBPs) and derive the operational matrices of integration and delays for these polynomials. Then, we apply them to convert the pantograph equations to a system of linear equations. ...
Non standard finite difference scheme preserving dynamical properties
We study the construction of a non-standard finite differences numerical scheme for a general class of two dimensional differential equations including several models in population dynamics using the idea of non-local approximation introduced by R. ...
Exponential fitting Runge-Kutta methods for the delayed recruitment/renewal equation
The so-called delayed recruitment/renewal equation provides the mathematical model in a diverse spectrum of practical applications and may become singularly perturbed when the time-lag is large relative to the reciprocal of the decay rate. In order to ...
Worst case error bounds for the solution of uncertain Poisson equations with mixed boundary conditions
Given linear elliptic partial differential equations with mixed boundary conditions, with uncertain parameters constrained by inequalities, we show how to use finite element approximations to compute worst case a posteriori error bounds for linear ...
A modified fifth-order WENOZ method for hyperbolic conservation laws
The paper analyses by Taylor series the several fifth-order of accuracy schemes for hyperbolic conservation laws: the classical WENOJS scheme Jiang and Shu (1996), the WENOM scheme Henrick et al. (2005), the WENOZ scheme Borges et al. (2008) and the ...
Structural credit risk modelling with Hawkes jump diffusion processes
To describe the unexpectedness of default and especially default clustering in the framework of Merton's structural default, we propose a novel jump diffusion model for the firm's value. In this model, the jumps, which reflect the systematic risk common ...
Upwind numerical approximations of a compressible 1d micropolar fluid flow
In this paper we consider the numerical approximations of the nonstationary 1D flow of a compressible micropolar fluid, which is in the thermodynamical sense perfect and polytropic. The flow equations are considered in the Eulerian formulation. It is ...
The method of steepest descent for estimating quadrature errors
This work presents an application of the method of steepest descent to estimate quadrature errors. The method is used to provide a unified approach to estimating the truncation errors which occur when Gauss-Legendre quadrature is used to evaluate the ...
A limited memory quasi-Newton trust-region method for box constrained optimization
By means of Wolfe conditions strategy, we propose a quasi-Newton trust-region method to solve box constrained optimization problems. This method is an adequate combination of the compact limited memory BFGS and the trust-region direction while the ...
A new compounding family of distributions
We propose a new four-parameter family of distributions by compounding the generalized gamma and power series distributions. The compounding procedure is based on the work by Marshall and Olkin (1997) and defines 76 sub-models. Further, it includes as ...
The error structure of the Douglas-Rachford splitting method for stiff linear problems
The Lie splitting algorithm is frequently used when splitting stiff ODEs or, more generally, dissipative evolution equations. It is unconditionally stable and is considered to be a robust choice of method in most settings. However, it possesses a rather ...
A new approach on the construction of trigonometrically fitted two step hybrid methods
The construction of trigonometrically fitted two step hybrid methods for the numerical solution of second-order initial value problems is considered. These methods are suitable for the numerical integration of problems with periodic or oscillatory ...
A reliable incremental method of computing the limit load in deformation plasticity based on compliance
The aim of this paper is to introduce an enhanced incremental procedure that can be used for the numerical evaluation and reliable estimation of the limit load. A conventional incremental method of limit analysis is based on parametrization of the ...
High order time discretization for backward semi-Lagrangian methods
We introduce different high order time discretization schemes for backward semi-Lagrangian methods. These schemes are based on multi-step schemes like Adams-Moulton and Adams-Bashforth schemes combined with backward finite difference schemes. We apply ...
An optimal cascadic multigrid method for the radiative transfer equation
This paper presents a fast and optimal multigrid solver for the radiative transfer equation. A discrete-ordinate discontinuous-streamline diffusion method is employed to discretize the radiative transfer equation. Instead of utilizing conventional ...
Adaptive cross approximation for ill-posed problems
Integral equations of the first kind with a smooth kernel and perturbed right-hand side, which represents available contaminated data, arise in many applications. Discretization gives rise to linear systems of equations with a matrix whose singular ...
Construction of high-order quadratically stable second-derivative general linear methods for the numerical integration of stiff ODEs
Theory of general linear methods (GLMs) for the numerical solution of autonomous system of ordinary differential equations of the form y ' = f ( y ) is extended to include the second derivative y = g ( y ) : = f ' ( y ) f ( y ) . This extension of GLMs ...
A discrete commutator theory for the consistency and phase error analysis of semi-discrete C 0 finite element approximations to the linear transport equation
A novel method, based on a discrete commutator, for the analysis of consistency error and phase relations for semi-discrete continuous finite element approximation of the one-way wave equation is presented. The technique generalizes to arbitrary ...