We report a new numerical algorithm for solving one-dimensional linear parabolic partial differential equations PDEs . The algorithm employs optimal quadratic spline collocation QSC for the space discretization and two-stage Gauss method for the time discretization. The new algorithm results in errors of fourth order at the gridpoints of both the space partition and the time partition, and larg...

We describe a hybrid modeling-discretization numerical method for approximating the solution of an elliptic problem with a discontinuous diffusion coefficient that is suited for cut-cell problems in which the discontinuity interface is not resolved by the mesh. The method is inspired by the well-known Ghost Fluid Method. We carry out an a posteriori error analysis for the numerical solution for...

A numerical method for computational implementation of gradient dynamical systems is presented. The method is based upon the development of geometric integration numerical methods, which aim at preserving the dynamical properties of the original ordinary differential equation under discretization. In particular, the proposed method belongs to the class of discrete gradients methods, which subst...

Abstrak Handling numerical data stored in a relational database is different from handling those numerical data stored in a single table due to the multiple occurrences of an individual record in the non-target table and non-determinate relations between tables. Most traditional data mining methods only deal with a single table and discretize columns that contain continuous numbers into nominal...

In this thesis, a high-order finite element scheme, based upon the Discontinuous Galerkin (DG) method, is introduced to solve oneand two-dimensional Elastohydrodynamic Lubrication (EHL) problems (line contact and point contact). This thesis provides an introduction to elastohydrodynamic lubrication, including some history, and a description of the underlying mathematical model which is based up...

We present an easy to implement drift splitting numerical method for the approximation of stiff, nonlinear stochastic differential equations (SDEs). The method is an adaptation of the semi-implicit backward differential formula (SBDF) multistep method for deterministic differential equations and allows for a semi-implicit discretization of the drift term to remove high order stability constrain...

We develop a Fourier method to solve backward stochastic differential equations (BSDEs). General theta-discretization of the time-integrands leads to an induction scheme with conditional expectations. These are approximated by using Fourier-cosine series expansions, relying on the availability of a characteristic function. The method is applied to BSDEs with jumps. Numerical experiments demonst...

Abstract: In this paper we develop a numerical algorithm that computes the Green’s function for a 2D finite-size photonic crystal, composed of rods of arbitrary shape. The method is based on boundary integral equation, and a Nyström discretization is used for the numerical solution. We derive multipole expansions for circular cylinders using our integral equation approach. Its numerical solutio...

In this work a new numerical method is constructed for time-integrating multidimensional parabolic semilinear problems in a very efficient way. The method reaches the fourth order in time and it can be combined with standard spatial discretizations of any order to obtain unconditinally convergent numerical algorithms. The main theoretical results which guarantee this property are explained here...

In this paper the method of integral equations is proposed for some problems of electrical engineering ( current density, radiative heat transfer, heat conduction). Presented models lead to a system of Fredholm integral equations, integro-differential equations or Volterra-Fredholm integral equations, respectively. We propose various numerical methods (discretization method and projection metho...