Finite Difference Methods, Theory and Applications

Simulation of Flow in Fractured Poroelastic Media: a Comparison of Different Discretization Approaches.- A Transparent Boundary Condition for an Elastic Bottom in Underwater Acoustics.- Well-Posedness in Holder Spaces of Elliptic Differential and Difference Equations.- Operator Semigroups for Convergence Analysis.- The Power of Trefftz Approximations: Finite Difference, Boundary Difference and Discontinuous Galerkin Methods; Nonreflecting Conditions and Non-Asymptotic Homogenization.- On Extension of Asymptotic Comparison Principle for Time Periodic Reaction-Diffusion-Advection Systems with Boundary and Internal Layers.- The Finite Difference Method for Boundary Value Problem with Singularity.- Superconvergence of Some Linear and Quadratic Functionals for Higher-order Finite Elements.- Time Step for Numerically Solving Parabolic Problems.- Recent Advances in Numerical Solution of HJB Equations Arising in Option Pricing.- Applications of Numerical Methods for Stochastic Controlled Switching Diffusions with A Hidden Markov Chain: Case Studies on Distributed Power Management and Communication Resource Allocation.- Error Estimates of the Crank-Nicolson-Polylinear FEM with the discrete TBC for the Generalized Schrodinger Equation in an Unbounded Parallelepiped.- Difference Schemes for Delay Parabolic Equations with Periodic Boundary Conditions.- Some Results of FEM Schemes Analysis by Finite Difference Method.- Application of Finite Difference TVD Methods in Hypersonic Aerodynamics.- Finite Difference Equations for Neutron Flux and Importance Distribution in 3D Heterogeneous Reactor.- Matrix-free Iterative Processes for Implementation of Implicit Runge-Kutta Methods.- Simulation of Technogenic and Climatic Influences in Permafrost.- Iterative Implicit Methods for Solving Nonlinear Dynamical Systems: Application of the Levitron.- Modeling Textile Fabric used in Pest Control with a 3 Scale Domain Decomposition Method.- The Theory and Applications of the SMIF Method for Correct Mathematical Modeling of the Incompressible Fluid Flows.- Determination of the Time-dependent Thermal Conductivity in the Heat Equation with Spacewise Dependent Heat Capacity.- Inverse Problems of Simultaneous Determination of the Time-dependent Right-hand Side Term and the Coefficient in a Parabolic Equation.- Effectiveness of the parallel implementation of the FEM for the problem of the surface waves propagation.- Splitting Scheme for Poroelasticity and Thermoelasticity Problems.