in this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. a fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. thomas algorithm is used to solve the tri-diagonal system. the stability of the algorithm is investigated. it ...

Let G be an affine group scheme of finite type over a global field F . (We do not assume G to be reductive or smooth or connected.) Let AF denote the locally compact adele ring of F , S be a finite non-empty set of places of F that contains the archimedean places, and AF the factor ring of adeles with vanishing component along S; for FS = ∏ v∈S Fv, we have AF = FS ×AF . Recall that if X is a fi...

We propose a novel high resolution conservative advection scheme that is suitable for thin, embedded moving solid structures. The scheme works by coupling together a high order flux-based method with a conservative semi-Lagrangian solver that is similar in spirit to that of [26], but modified to treat the cut cells and partial volumes that arise near a thin solid structure. The conservative sem...

In this paper, a Chebyshev finite difference method has been proposed in order to solve nonlinear two-point boundary value problems for second order nonlinear differential equations. A problem arising from chemical reactor theory is then considered. The approach consists of reducing the problem to a set of algebraic equations. This method can be regarded as a non-uniform finite difference schem...

In this paper a finite difference method for solving 2-dimensional diffusion equation is presented. The method employs Crank-Nicolson scheme to improve finite difference formulation and its convergence and stability. The obtained solution will be a recursive formula in each step of which a system of linear equations should be solved. Given the specific form of obtained matrices, rather than sol...

A unified framework to derive optimized compact schemes for a uniform grid is presented. The scheme coefficients are determined analytically by solving an optimization problem minimize the spectral error subject equality constraints that ensure specified order of accuracy. rigorous stability analysis also We show other types e.g., spatially explicit and biased finite differences, can be generat...