Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators desirable their stability properties, significantly relaxing restrictions on timestep size. However, implicit require solutions to one or more systems nonlinear equations at each timestep, which large simulations can be prohibitively ex...

Bus network design is an important problem in public transportation. A main step to this design is determining the number of required terminals and their locations. This is a special type of facility location problem, which is a time-consuming, large scale, combinatorial problem. In a previous attempt by the authors, this problem had been solved by GAMS, based on a branch and bound algorithm. ...

in this paper an efficient dual time implicit approach is used to solve viscous laminar flow around two bodies with general motion. therefore, the grid includes a background grid and two sets of grids around the moving bodies. rotational and translational motions of two bodies are managed separately in this grid arrangement. in this work the overset concept for hybrid grid is used and flow vari...

Bus network design is an important problem in public transportation. A main step to this design is determining the number of required terminals and their locations. This is a special type of facility location problem, which is a time-consuming, large scale, combinatorial problem. In a previous attempt by the authors, this problem had been solved by GAMS, based on a branch and bound algorithm.&...

Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...

This paper constructs extrapolated implicit-explicit time stepping methods that allow one to efficiently solve problems with both stiff and nonstiff components. The proposed methods are based on Euler steps and can provide very high order discretizations of ODEs, index-1 DAEs, and PDEs in the method of lines framework. Implicit-explicit schemes based on extrapolation are simple to construct, ea...