Wavelet analysis provides information on the energy present at various scales and locations throughout a computational domain. This information is precisely the information that is needed to define the appropriate gridpoint densities and the appropriate numerical order to resolve the physics at hand in the computationally most efficient manner. Here a two-dimensional version of the numerical me...

A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter. These parameters are assumed to be distinct. The components of the solution exhibit overlapping layers. Shishkin piecewise-uniform meshes are introduced, which ...

We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV transmission dynamics. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves the positivity of...

In this article a numerical method involving classical finite difference scheme on non-uniform grid is constructed for a singularly perturbed convection-diffusion boundary value problem with two small parameters affecting the convection and diffusion terms. The scheme has been analyzed for uniform convergence with respect to both singular perturbation parameters. To support the theoretical erro...

In this paper, Numerical Methods for solving ordinary differential equations, beginning with basic techniques of finite difference methods for linear boundary value problem is investigated. Numerical solution is found for the boundary value problem using finite difference method and the results are compared with analytical solution. MATLAB coding is developed for the finite difference method. T...

In this paper, we present a numerical approach to a class of nonlinear reactiondiffusion equations with nonlocal Robin type boundary conditions by finite difference methods. A second-order accurate difference scheme is derived by the method of reduction of order. Moreover, we prove that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete L2-norm. ...

We develop a new efficient second-order finite difference scheme for two-dimensional problem of contaminant in groundwater flow. Theoretical analysis shows that the scheme is second-order convergence in the L2 norm and is unconditionally stable. Numerical results demonstrate that the error measures of the second-order scheme are several times smaller than those of the standard implicit finite d...

A conservative three-level linear finite difference scheme for the numerical solution of the initial-boundary value problem of Rosenau-KdV equation is proposed.The difference scheme simulates two conservative quantities of the problemwell.The existence and uniqueness of the difference solution are proved. It is shown that the finite difference scheme is of second-order convergence and unconditi...

In this work, we propose a model of nonlocal partial differential equation (PDE) with deviated type function in the boundary condition. This model is solved numerically by finite difference method (FDM) using variable space grid (VSG) technique. The results obtained by this method are in a good agreement with the solution of the corresponding rectangular domain problem. Also, we investigated th...