There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

高等学校計算数学学報 = Numerical mathematics

Diffusion and ecological problems : mathematical models

This review is an elementary introduction to the concepts of the recently developed asymptotic methods and new developments. Particular attention is paid throughout the paper to giving an intuitive grasp for Lagrange multiplier, calculus of variations, optimization, variational iteration method, parameter-expansion method, exp-function method, homotopy perturbation method, and ancient Chinese mathematics as well. Subsequently, nanomechanics in textile engineering and E-innit y theory in high energy physics, Kleiber’s 3/4 law in biology, possible mechanism in spider-spinning process and fractal approach to carbon nanotube are briey introduced. Bubble-electrospinning for mass production of nanob ers is illustrated. There are in total more than 280 references.

An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering

A numerical method based on the Adomian decomposition method which has been developed by Adomian [Adomian, G. (1994). Solving Frontier Problems of Physics: The Decomposition Method. Kluwer Academic Publishers, Boston, MA] is introduced in this paper for the approximate solution of delay differential equations. The algorithm is illustrated by studying an initial value problem. The results obtained are presented and show that only a few terms are required to obtain an approximate solution which is found to be accurate and efficient.

The Adomian decomposition method for solving delay differential equation

Adomian decomposition method for Burger's-Huxley and Burger's-Fisher equations

Exact solutions of some important nonlinear partial differential equations are obtained by using the first integral method. The efficiency of the method is demonstrated by applying it for two selected equations.

The first integral method for solving some important nonlinear partial differential equations

A collocation method with cubic B-splines for solving the MRLW equation

In this paper, we established a traveling wave solution by using the modified extended tanh method for space-time fractional nonlinear partial differential equations. The method is used to obtain exact solutions for different types of space-time fractional nonlinear partial differential equations such as space-time fractional equal width wave equation (EWE) and space-time fractional modified equal width wave equation (MEW) which are important soliton equations. Both equations are reduced to ordinary differential equations by using fractional complex transform and properties of modified Riemann-Liouville derivative. We plot the exact solutions for these equations at different time levels.

Kamal R. Raslan

Papers

The Adomian decomposition method for solving delay differential equation

Adomian decomposition method for Burger's-Huxley and Burger's-Fisher equations

The first integral method for solving some important nonlinear partial differential equations

A collocation method with cubic B-splines for solving the MRLW equation

The modified extended tanh method with the Riccati equation for solving the space-time fractional EW and MEW equations