In this study, the general partial differential equation of unsteady groundwater flow through non-homogeneous and anisotropic aquifer was solved by the fully implicit finite difference method with control volume approach. The calibration of permeability and storage coefficients as model parameters was performed by a transformation technique and application of Powell's non-linear optimization me...

We prove the generalized Hyers--Ulam stability  of $n$-th order linear differential equation of the form $$y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x),$$ with condition that there exists a non--zero solution of corresponding homogeneous equation. Our main results extend and improve the corresponding results obtained by many authors.

Discrete forms of the Schrödinger equation, the diffusion equation, the linearized Landau-Ginzburg equation, and discrete models for vibrations and spin dynamics belong to a class of Laplacian-based finite difference models. Real-space renormalization of such models on finitely ramified regular fractals is known to give exact recursion relations. It is shown that these recursions commute with L...

a numerical study of 3d electrokinetic flows through micromixers was performed. the micromixers considered here consisted of heterogeneous rectangular microchannels with prescribed patterns of zeta-potential at their walls. numerical simulation of electroosmotic flows within heterogeneous channels requires solution of the navier-stokes, ernest-plank and species concentration equations. it is kn...

The Schur algorithm and its times-domain counterpart, the fast Cholseky recursions, are some efficient signal processing algorithms which are well adapted to the study of inverse scattering problems. These algorithms use a layer stripping approach to reconstruct a lossless scattering medium described by symmetric two-component wave equations which model the interaction of right and left propaga...

Best mean square prediction for moving average time series models is generally non-linear prediction, even in the invertible case. Gaussian processes are an exception, since best linear prediction is always best mean square prediction. Stable numerical recursions are proposed for computation of residuals and evaluation of unnormalized conditional distributions in invertible or non-invertible mo...

reservoir models with many grid blocks suffer from long run time; it is hence important to deliberatea method to remedy this drawback. usual upscaling methods are proved to fail to reproduce fine gridmodel behaviors in coarse grid models in well proximity. this is attributed to rapid pressure changesin the near-well region. standard permeability upscaling methods are limited to systems with lin...