The finite analytic numerical method is developed to solve two-point boundary value problems of ordinary differential equations. The basic idea of the finite analytic method is the incorporation of the local analytic solution of the governing equation in the numerical solution of the boundary value problem. In this study, the finite analytic solution is developed for both linear and nonlinear s...

In this paper we present a stable hybrid scheme for viscous problems. The hybrid method combines the unstructured finite volume method with high-order finite difference methods in complex geometries. The coupling procedure between the two numerical methods is based on energy estimates and stable interface conditions are constructed. Numerical calculations show that the hybrid method is efficien...

flood routing has many applications in engineering projects and helps designers in understanding the flood flow characteristics in river flows. floods are taken unsteady flows that vary by time and location. equations governing unsteady flows in waterways are continuity and momentum equations which in case of one-dimensional flow the saint-venant hypothesis is considered. dynamic wave model as ...

In this paper a singularly perturbed reaction-diffusion partial differential equation in two space dimensions is examined. By means of an appropriate decomposition, we describe the asymptotic behaviour of the solution of problems of this kind. A central finite difference scheme is constructed for this problem which involves an appropriate Shishkin mesh. We prove that the numerical approximation...

Abstract. The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the numerical error is taken into account. The theoretical study of a related linear algebraic problem gives general results which can lead to the dete...

We study compact finite difference methods for the Schrödinger-Poisson equation in a bounded domain and establish their optimal error estimates under proper regularity assumptions on wave function ψ and external potential V(x). The CrankNicolson compact finite difference method and the semi-implicit compact finite difference method are both of order O(h4+τ2) in discrete l2 ,H1 and l norms with ...

This paper deals with application of the maximum principle for differential equations to the finite difference method for determining upper and lower approximate solutions of the non-linear Burgers’ equation and their error range. In term of mathematical architecture, the paper is based on the maximum principle for parabolic differential equations to establish monotonic residual relations of th...

In this paper we discuss the problem of an adaptive parameter choice in onesided finite difference schemes for the numerical differentiation in case when noisy values of the function to be differentiated are available only at the given points. This problem is motivated by diabetes therapy management, where it is important to provide estimations of the future blood glucose trend from current and...

A system of singularly perturbed ordinary differential equations of first order with given initial conditions is considered. The leading term of each equation is multiplied by a small positive parameter. These parameters are assumed to be distinct and they determine the different scales in the solution to this problem. A Shishkin piecewise–uniform mesh is constructed, which is used, in conjunct...