Improved G\u27/G-Expansion Method and Comparing with Tanh-Coth Method

In this paper, improved G\u27/G-expansion and tanh-coth methods for solving partial differential equations are compared. It has been shown that the tanh-coth method is a special case of the improved G\u27/G-expansion method. For illustration and more explanation of the idea, exact solutions of the Burgers and Boussinesq equations are obtained by improved G\u27/G-expansion and the results obtained compared with those of tanh-coth method

An Efficient Technique for Solving Special Integral Equations

In this paper, we apply a new technique for solving two-dimensional integral equations of mixed type. Comparisons are made between the homotopy perturbation method and the new technique. The results reveal that the new technique is effective and convenient

(R1458) A New Finite Difference Scheme for High-Dimensional Heat Equation

In this research‎, ‎a new second-order finite difference scheme is proposed to solve two and three- dimensional heat equation‎. Finite difference equations are determined via a discretization approach in which spatial second order partial derivatives in x and y directions are approximated simultaneously‎ while in the classic method, each spatial partial derivative is replaced by a central finite difference approximation, separately. By this new discretization scheme and also using the forward difference to the first-order time derivative, a finite difference equation is obtained for the parabolic equation. This approach is explicit and similar to other explicit approaches, an interval for the Courant number, r is determined. This region for r is obtained through Fourier stability analysis. The advantage of this approach is that its stability interval is larger than the interval for traditional methods. Numerical experiments are presented to confirm the theoretical results‎. It is shown that more accurate approximations can be obtained by the new scheme

A new third-order family of nonlinear solvers for multiple roots

AbstractIn this paper, a new family of third-order methods for finding multiple roots of nonlinear equations has been introduced. This family requires one-function and two-derivative evaluation per iteration. The family contains several known third-order methods, as special cases. Some examples are presented to show the performance of the presented family

Redistribution of Nodes with Two Constraints in Meshless Method of Line to Time-Dependent Partial Differential Equations

Meshless method of line is a powerful device to solve time-dependent partial differential equations. In integrating step, choosing a suitable set of points, such as adaptive nodes in spatial domain, can be useful, although in some cases this can cause ill-conditioning. In this paper, to produce smooth adaptive points in each step of the method, two constraints are enforced in Equidistribution algorithm. These constraints lead to two different meshes known as quasi-uniform and locally bounded meshes. These avoid the ill-conditioning in applying radial basis functions. Moreover, to generate more smooth adaptive meshes another modification is investigated, such as using modified arc-length monitor function in Equidistribution algorithm. Influence of them in growing the accuracy is investigated by some numerical examples. The results of consideration of two constraints are compared with each other and also with uniform meshes

Some Higher-Order Families of Methods for Finding Simple Roots of Nonlinear Equations

Abstract In this paper, a new fifth-order family of methods fre

Numerical solution of functional integral equations by the variational iteration method

AbstractIn the present article, we apply the variational iteration method to obtain the numerical solution of the functional integral equations. This method does not need to be dependent on linearization, weak nonlinearity assumptions or perturbation theory. Application of this method in finding the approximate solution of some examples confirms its validity. The results seem to show that the method is very effective and convenient for solving such equations

Nanotoxicology and nanoparticle safety in biomedical designs

Nanotechnology has wide applications in many fields, especially in the biological sciences and medicine. Nanomaterials are applied as coating materials or in treatment and diagnosis. Nanoparticles such as titania, zirconia, silver, diamonds, iron oxides, carbon nanotubes, and biodegradable polymers have been studied in diagnosis and treatment. Many of these nanoparticles may have toxic effects on cells. Many factors such as size, inherent properties, and surface chemistry may cause nanoparticle toxicity. There are methods for improving the performance and reducing toxicity of nanoparticles in medical design, such as biocompatible coating materials or biodegradable/biocompatible nanoparticles. Most metal oxide nanoparticles show toxic effects, but no toxic effects have been observed with biocompatible coatings. Biodegradable nanoparticles are also used in the efficient design of medical materials, which will be reviewed in this article

Optimal Homotopy Asymptotic and Multistage Optimal Homotopy Asymptotic Methods for Solving System of Volterra Integral Equations of the Second Kind

In this paper, optimal homotopy asymptotic method (OHAM) and its implementation on subinterval, called multistage optimal homotopy asymptotic method (MOHAM), are presented for solving linear and nonlinear systems of Volterra integral equations of the second kind. To illustrate these approaches two examples are presented. The results confirm the efficiency and ability of these methods for such equations. The results will be compared to find out which method is more accurate. Advantages of applying MOHAM are also illustrated