in this article we have considered a non-standard finite difference method for the solution of second order  fredholm integro differential equation type initial value problems. the non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the fredholm integro-differential equation into a system of equations. we have also developed a numerical met...

in recent years, the number of research works devoted to applying the highly accurate numerical schemes, in particular compact finite difference schemes, to numerical simulation of complex flow fields with multi-scale structures, is increasing. the use of compact finite-difference schemes are the simple and powerful ways to reach the objectives of high accuracy and low computational cost. compa...

in this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. the numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. in order to get a numerical solution for the derivative of the solution, the given interval is divided  in...

We study an optimal control problem for viscosity solutions of a Hamilton-Jacobi equation describing the propagation of a one dimensional graph with the control being the speed function. The existence of an optimal control is proved together with an approximate controllability result in the H−1 norm. We prove convergence of a discrete optimal control problem based on a monotone finite differenc...

In this article we have considered a non-standard finite difference method for the solution of second order  Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the Fredholm integro-differential equation into a system of equations. We have also developed a numerical met...

The numerical solution of a model describing a two-dimensional fluidized bed by a Chebyshev super spectral viscosity (SSV) method is considered. The model is in the form of a hyperbolic system of conservation laws with a source term, coupled with an elliptic equation for determining a stream function. The coupled elliptic equation is solved by a finite difference method. The mixed SSV/finite di...

In this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided  in...

We consider a situation where dislocations are parallel lines moving in a single plane. For this simple geometry, dislocations dynamics is modeled by a one-dimensional non-local transport equation. We prove a result of existence and uniqueness for all time of the continuous viscosity solution for this equation. A finite difference scheme is proposed to approximate the continuous viscosity solut...

the compact finite difference schemes have been found to give simple ways of reaching the objectives of high accuracy and low computational cost. during the past two decades, the compact schemes have been used extensively for numerical simulation of various fluid dynamics problems. these methods have also been applied for numerical solution of some prototype geophysical fluid dynamics problems ...