In this study, a first-order, nonstationary stochastic model of transient flow is developed which is applicable to the entire domain of a bounded vadose zone in the presence of sink/source. We derive general equations governing the statistical moments of the flow quantities by perturbation expansions. Owing to the mathematical complexity of the equations, in general we need to solve them numeri...

In this paper, we develop a two-stage numerical method for computing the approximate solutions of third-order boundary-value problems associated with odd-order obstacle problems. We show that the present method is of order two. A numerical example is presented to illustrate the applicability of the new method. A comparison is also given with previously known results.

The solution of the heat conduction probem in moving boundary conditions is very important in predicting accurate thermal behavior of materials when very high energy deposition is expected. Such high fluxes are encountered on first wall materials and other components in fusion reactors. A numerical method has been developed to solve this problem by the use of the Green's function. A comparison ...

Elliptic problems with sharp-edged interfaces, thin-layered interfaces and interfaces that intersect with geometric boundary, are notoriously challenging to existing numerical methods, particularly when the solution is highly oscillatory. This work generalizes the matched interface and boundary (MIB) method previously designed for solving elliptic problems with curved interfaces to the aforemen...

Submitted for the DPP13 Meeting of The American Physical Society Finite Volume Scheme for Anisotropic Diffusion1 BRAM VAN ES, CWI, Amsterdam, The Netherlands; FOM Institute DIFFER, Nieuwegein, The Netherlands, BARRY KOREN, CWI, Amsterdam, The Netherlands; Eindhoven University of Technology, Eindhoven, The Netherlands, HUGO DE BLANK, FOM Institute DIFFER, Nieuwegein, The Netherlands — In fusion ...

In this paper, we formulate a fractional thermal wave model for a bi-layered spherical tissue. Implicit finite difference method is employed to obtain the solution of the direct problem. The inverse analysis for simultaneously estimating the Caputo fractional derivative and the relaxation time parameters is implemented by means of the Levenberg–Marquardt method. Compared with the experimental d...

In this paper, we present a numerical solution to an ordinary differential equation of a fractional order in one-dimensional space. The solution to this equation can describe a steady state of the process of anomalous diffusion. The process arises from interactions within complex and non-homogeneous background. We present a numerical method which is based on the finite differences method. We co...

Various fields of science and engineering deal with dynamical systems that can be described by fractional partial differential equations (FPDE), for example, systems biology, chemistry and biochemistry applications due to anomalous diffusion effects in constrained environments. However, effective numerical methods and numerical analysis for FPDE are still in their infancy. In this paper, we con...

Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initialboundary value fractional partial differential equations with variable coefficients on a finite domain. We ...

Using classical finite difference schemes often generates numerical drawbacks such as spurious oscillations in the solution of the famous Black–Scholes partial differential equation. We analyze the fully implicit scheme, frequently used numerical method in Finance, that in the presence of discontinuous payoff and low volatility arises spurious oscillations. We propose a modification of this sch...