A Note on He’s Parameter-Expansion Method of Coupled Van der Pol–Duffing Oscillators

This paper presents the analytical and approximate solutions of the coupled chaotic Van der Pol-Duffing systems, by using the He\u27s parameter-expansion method (PEM). One iteration is sufficient to obtain a highly accurate solution, which is valid for the whole solution domain. From the obtained results, we can conclude that the suggest method, is of utter simplicity, and can be easily extended to all kinds of non-linear equations

Numerical Simulations of Some Real-Life Problems Governed by ODEs

In this chapter, some real-life model problems that can be formulated as ordinary differential equations (ODEs) are introduced and numerically studied. These models are the variable-order fractional Hodgkin–Huxley model of neuronal excitation (VOFHHM) and other models with the variable-order fractional (VOF) time delay, such as the 4-year life cycle of a population of lemmings model, the enzyme kinetics with an inhibitor molecule model, and the Chen system model. A class of numerical methods is used to study the above-mentioned models such as non-standard finite difference (NSFD) and Adams-Bashforth-Moulton (ABM) methods. Numerical test examples are presented

On the numerical simulation of population dynamics with density-dependent migrations and the Allee effects

In this paper, the variational iteration method (VIM) and the Adomian decomposition method (ADM) are presented for the numerical simulation of the population dynamics model with density-dependent migrations and the Allee effects. The convergence of ADM is proved for the model problem. The results obtained by these methods are compared to the exact solution. It is found that these methods are always converges to the right solutions with high accuracy. Furthermore, VIM needs relative less computational work than ADM

Numerical Studies for Solving Fractional Riccati Differential Equation

In this paper, finite difference method (FDM) and Pade\u27-variational iteration method (Pade\u27- VIM) are successfully implemented for solving the nonlinear fractional Riccati differential equation. The fractional derivative is described in the Caputo sense. The existence and the uniqueness of the proposed problem are given. The resulting nonlinear system of algebraic equations from FDM is solved by using Newton iteration method; moreover the condition of convergence is verified. The convergence\u27s domain of the solution is improved and enlarged by Pade\u27-VIM technique. The results obtained by using FDM is compared with Pade\u27-VIM. It should be noted that the Pade\u27-VIM is preferable because it always converges to the solution even for large domain

Numerical Simulation for Solving Fractional Riccati and Logistic Differential Equations as a Difference Equation

In this paper, we introduce a numerical treatment using the generalized Euler method (GEM) for the fractional (Caputo sense) Riccati and Logistic differential equations. In the proposed method, we invert the given model as a difference equation. We compare our numerical solutions with the exact solution and with those numerical solutions using the fourth-order Runge-Kutta method (RK4). The obtained numerical results of the two proposed problem models show the simplicity and efficiency of the proposed method

Semi-Analytical Solution for the Multicell Spheroid model for Vascular Tumor Growth

Abstract: The homotopy analysis method is used to obtain semi-analytic solutions for the mathematical model describing a solid tumor growth in the initial a vascular stage of growth. During a vascular tumor growth, the balance between cell proliferation and cell loss determines whether the colony expands or progress. We focus on the chemical inhibition of mitosis within multicell spheroids. The main assumption of modeling the diffusion of a growth inhibitory factor (GIF) within a multicell spheroid and its possible effects on cell mitosis and proliferation

Impact of full-scale models on students’ creativity in basic design course

Designing and implementing full-scale models by architecture students is one of the most difficult and uncommon experiences in design education. The study evaluates the impact of this experience on the development of creative design skills among first-year students. This is achieved by applying a methodology that combines quantitative analysis of learning outcomes, especially those associated with the skills of Basic Design courses, with qualitative analysis of sketches, scaled and full models, and video recordings of students during design and implementation stages. This study provides experimental support for the use of full-scale models in design education to develop students’ creative skills, in addition to discussing opportunities and challenges to help faculty and researchers in the field of design education

Cryoglobulinaemia in Egyptian Patients with Extrahepatic Cutaneous Manifestations of Chronic Hepatitis C Virus Infection

Background. Hepatitis C is a global major health problem with extremely variable extrahepatic manifestations. Mixed cryoglobulinaemia (MC) shows a striking association with hepatitis C virus (HCV) infection, and it is sometimes asymptomatic. The skin is a frequently involved target organ in MC. Objective. To investigate the prevalence of cryoglobulinaemia in a sample of Egyptian patients with cutaneous manifestations of chronic HCV infection and to correlate its presence with clinical criteria and liver function tests. Methods. One hundred and eighteen patients with skin manifestations of chronic compensated hepatitis C were included. Venous blood was tested for liver function tests and serum cryoglobulins. Results. Twelve patients (10.169%) were positive for serum cryoglobulins (2 with pruritus, 4 with vasculitic lesions, 3 with livedo reticularis, one with oral lichen, one with chronic urticaria, and another with Schamberg’s disease). Vasculitic lesions and livedo reticularis of the legs showed higher prevalence in cryoglobulin-positive than in cryoglobulin-negative patients. Presence of serum cryoglobulins did not relate to patients’ demographic or laboratory findings. Conclusions. Fortunately, MC is not markedly prevalent among Egyptians with cutaneous lesions of chronic hepatitis C, and cryopositivity was commonly, but not exclusively, detected with cutaneous vasculitis and livedo reticularis. Laboratory testing for cryoglobulins in every HCV patient is advisable for earlier MC detection and management