A new numerical method is presented for the heat equation with discontinuous coefficients based on a Crank–Nicolson scheme and a conforming finite element space discretization. In the proposed method each node of the spatial discretization may have the global timestep split into an arbitrary number of local substeps in order to pursue a local improvement of the time discretization in the region...

In this paper we develop and analyze an efficient computational method for solving stochastic optimal control problems constrained by elliptic partial differential equation (PDE) with random input data. We first prove both existence and uniqueness of the optimal solution. Regularity of the optimal solution in the stochastic space is studied in view of the analysis of stochastic approximation er...

Abstract: In this paper Differential Transform Method (DTM) is implemented to solve some Riccati differential equations with variable co-efficients. This technique doesn’t require any discretization, linearization or small perturbations and therefore it reduces significantly the numerical computation. The results derived by this method are compared with the numerical results by Runge Kutta 4 (R...

Many problems of interest in science and engineering involve several types of physics possibly interacting over several scales in time and space. This minisymposia presents recent progress on numerical methods for solving problems involving multiple scales and/or physics. In particular, topics include adaptive procedures for tuning critical discretization parameters, technology for treating mul...

A conservative modification to the ghost fluid method (GFM) is developed for compressible multiphase flows. The motivation is to eliminate or reduce the conservation error of the GFM without affecting its performance. We track the conservative variables near the interface and use this information to modify the numerical solution when the interface has passed the cell. The modification procedure...

When random variables possessing arbitrary distribution functions must be added, subtracted, multiplied, etc., Monte Carlo simulation is commonly employed. However, Monte Carlo simulation typically assumes that the distribution functions to be combined are independent, and must assume either independence or some other specific dependency relationship. Discretization of the distribution function...

In this paper we propose a wavelet Taylor–Galerkin method for the numerical solution of time-dependent advection–di usion problems. The discretization in time is performed before the spatial discretization by introducing secondand third-order accurate generalization of the standard time stepping schemes with the help of Taylor series expansions in time step. Numerical schemes taking advantage o...

The goal of this article is to simulate rotating flows of shallow layers of fluid by means of finite volume numerical schemes. More precisely, we focus on the simulation of the geostrophic adjustment phenomenon. As spatial discretization, a first order Roe-type method and some higher order extensions are developed. The time discretization is designed in order to provide suitable approximations ...

We propose a numerical algorithm for finding the steady-state queue occupancy distribution for a workload-dependent MAP/PH/1 queue in which the arrival process and the service rate depend continuously on the instantaneous workload in the system. Both infinite and finite queue capacity scenarios are considered, including partial rejection and complete rejection policies for the latter. Using dis...

In this study we develop high order numerical methods to capture the spatiotemporal dynamics of a generalized Kolmogorov-Petrovskii-Piskunov (KPP) equation characterized by density dependent non-linear diffusion. Towards this direction we consider third order Strong Stability Preserving Runge-Kutta (SSPRK) temporal discretization schemes coupled with the fourth order Hermite cubic Collocation (...