Abstract: This paper presents a finite point method based on
directional derivatives for diffusion equation on 2D scattered points.
To discretize the diffusion operator at a given point, a six-point stencil
is derived by employing explicit numerical formulae of directional
derivatives, namely, for the point under consideration, only five
neighbor points are involved, the number of which is the smallest for
discretizing diffusion operator with first-order accuracy. A method for
selecting neighbor point set is proposed, which satisfies the solvability
condition of numerical derivatives. Some numerical examples are
performed to show the good performance of the proposed method.
Abstract: In this paper, we develop an accurate and efficient Haar wavelet method for well-known FitzHugh-Nagumo equation. The proposed scheme can be used to a wide class of nonlinear reaction-diffusion equations. The power of this manageable method is confirmed. Moreover the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.
Abstract: Water pollution assessment problems arise frequently
in environmental science. In this research, a finite difference method
for solving the one-dimensional steady convection-diffusion equation
with variable coefficients is proposed; it is then used to optimize
water treatment costs.
Abstract: In cancer progress, the optical properties of tissues
like absorption and scattering coefficient change, so by these
changes, we can trace the progress of cancer, even it can be applied
for pre-detection of cancer. In this paper, we investigate the effects of
changes of optical properties on light penetrated into tissues. The
diffusion equation is widely used to simulate light propagation into
biological tissues. In this study, the boundary integral method (BIM)
is used to solve the diffusion equation. We illustrate that the changes
of optical properties can modified the reflectance or penetrating light.
Abstract: In this paper we present modeling and simulation for
physical vapor deposition for metallic bipolar plates. In the models
we discuss the application of different models to simulate the
transport of chemical reactions of the gas species in the gas chamber.
The so called sputter process is an extremely sensitive process to
deposit thin layers to metallic plates. We have taken into account
lower order models to obtain first results with respect to the gas
fluxes and the kinetics in the chamber.
The model equations can be treated analytically in some
circumstances and complicated multi-dimensional models are solved
numerically with a software-package (UG unstructed grids, see [1]).
Because of multi-scaling and multi-physical behavior of the models,
we discuss adapted schemes to solve more accurate in the different
domains and scales. The results are discussed with physical
experiments to give a valid model for the assumed growth of thin
layers.
Abstract: Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper, a numerical solution for the one-dimensional hyperbolic telegraph equation by using the collocation method using the septic splines is proposed. The scheme works in a similar fashion as finite difference methods. Test problems are used to validate our scheme by calculate L2-norm and L∞-norm. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.
Abstract: Calcium is a vital second messenger used in signal transduction. Calcium controls secretion, cell movement, muscular contraction, cell differentiation, ciliary beating and so on. Two theories have been used to simplify the system of reaction-diffusion equations of calcium into a single equation. One is excess buffer approximation (EBA) which assumes that mobile buffer is present in excess and cannot be saturated. The other is rapid buffer approximation (RBA), which assumes that calcium binding to buffer is rapid compared to calcium diffusion rate. In the present work, attempt has been made to develop a model for calcium diffusion under excess buffer approximation in neuron cells. This model incorporates the effect of [Na+] influx on [Ca2+] diffusion,variable calcium and sodium sources, sodium-calcium exchange protein, Sarcolemmal Calcium ATPase pump, sodium and calcium channels. The proposed mathematical model leads to a system of partial differential equations which have been solved numerically using Forward Time Centered Space (FTCS) approach. The numerical results have been used to study the relationships among different types of parameters such as buffer concentration, association rate, calcium permeability.