A non-oscillatory numerical scheme based on a general solution of unsteady advection–di usion equations is presented. A general solution for initial value problems of linear two-dimensional unsteady advection–di usion equations is obtained using the spectral method. The resulting numerical scheme is explicit with respect to time, and ful lls the Patankar’s positive coe cients condition for any ...

We proposed a higher-order accurate explicit finite-difference scheme for solving the two-dimensional heat equation. It has a fourth-order approximation in the space variables, and a secondorder approximation in the time variable. As an application, we developed the proposed numerical scheme for solving a numerical solution of the two-dimensional coupled Burgers’ equations. The main advantages ...

in this paper by using the idea of mean convergence, weintroduce an iterative scheme for finding a common element of theset of solutions of an equilibrium problem and the fixed points setof a nonspreading-type mappings in hilbert space. a strongconvergence theorem of the proposed iterative scheme is establishedunder some control conditions. the main result of this paper extendthe results obtain...

finding a suitable estimation of stability domain around stable equilibrium points is an important issue in the study of nonlinear dynamical systems. this paper intends to apply a set of analytical-numerical methods to estimate the region of attraction for autonomous nonlinear systems. in mechanical and structural engineering, autonomous systems could be found in large deformation problems or c...

the transport of dissolved contaminants in groundwater is usually described by the advectiondispersion equation with reaction. several numerical methods for solving the one-dimensional are availableincluding finite difference methods, finite volume methods, and finite element methods. stringent conditions,such as small peclet (pe) and courant (cr) numbers, must be satisfied to ensure the accura...

Integrating various suppliers to satisfy market demand is of great importance for e ective supply chain management. In this paper, we consider the ODE-PDE model of supply chain and apply a classical explicit fourth-order Runge-Kutta scheme for the related ODE model of suppliers. Also, the convergence of the proposed method is proved. Finally a numerical example is studied to demonstrate the acc...