A Numerical Solution to Fractional Diffusion Equation for Force-Free Case

A collocation finite element method for solving fractional diffusion equation for force-free case is considered. In this paper, we develop an approximation method based on collocation finite elements by cubic B-spline functions to solve fractional diffusion equation for force-free case formulated with Riemann-Liouville operator. Some numerical examples of interest are provided to show the accuracy of the method. A comparison between exact analytical solution and a numerical one has been made

Aqueductal developmental venous anomaly as an unusual cause of congenital hydrocephalus: a case report and review of the literature

<p>Abstract</p> <p>Introduction</p> <p>Aqueductal stenosis may be caused by a number of etiologies including congenital stenosis, tumor, inflammation, and, very rarely, vascular malformation. However, aqueductal stenosis caused by a developmental venous anomaly presenting as congenital hydrocephalus is even more rare, and, to the best of our knowledge, has not yet been reported in the literature. In this study, we review the literature and report the first case of congenital hydrocephalus associated with aqueductal stenosis from a developmental venous anomaly.</p> <p>Case presentation</p> <p>The patient is a three-day-old, African-American baby girl with a prenatal diagnosis of hydrocephalus. She presented with a full fontanelle, splayed sutures, and macrocephaly. Postnatal magnetic resonance imaging showed triventricular hydrocephalus, suggesting aqueductal stenosis. Examination of the T1-weighted sagittal magnetic resonance imaging enhanced with gadolinium revealed a developmental venous anomaly passing through the orifice of the aqueduct. We treated the patient with a ventriculoperitoneal shunt.</p> <p>Conclusions</p> <p>Ten cases of aqueductal stenosis due to venous lesions have been reported and, although these venous angiomas and developmental venous anomalies are usually considered congenital lesions, all 10 cases became symptomatic as older children and adults. Our case is the first in which aqueductal stenosis caused by a developmental venous anomaly presents as congenital hydrocephalus. We hope adding to the literature will improve understanding of this very uncommon cause of hydrocephalus and, therefore, will aid in treatment.</p

Feelings of burden among family caregivers of people with spinal cord injury in Turkey

Study design: The study was designed as a cross-sectional survey. Objectives: The purpose of the study was to examine the level of feelings of burden in family caregivers of people with spinal cord injury (SCI) in Turkey, and to explore its predictors. Setting: Turkey. Methods: One hundred family caregivers of people with SCI completed measures of burden of caregiving, depression, social support and physical health. The SCI participants completed a measure of functional independence. Multivariate statistics and structural equation modeling (SEM) were conducted to identify significant predictors of caregiver burden. Results: Caregiver burden was significantly related to caregivers’ feelings of depression. SEM analysis showed that social support from family and from friends predicted caregiver burden via depression. Caregivers’ age, sex, educational level, physical health and household income did not significantly predict their feelings of depression or burden. Conclusions: Our findings revealed that support received from both families and friends is an important source for alleviating the depressive feelings of caregivers and, in return, their burden in the caregiving. In Turkey, high support from family members is expected and is important for psychological well-being, yet the current study showed that the support received from friends also has unique contribution to the well-being of the caregivers of persons with SCI. Overall, our findings highlight the importance of supportive relationships between family as well as friends for the caregivers who may have to provide lifetime care for their family member with special needs.WOS:000407265700012Scopus - Affiliation ID: 60105072PMID: 28169295Science Citation Index Expanded - Social Sciences Citation IndexQ2 - Q3ArticleUluslararası işbirliği ile yapılan - EVETAğustos2017YÖK - 2016-1

Approximate Analytical Solution to Time-Fractional Damped Burger and Cahn-Allen Equations

Cahn-Allen equations by means of the homotopy analysis method (HAM). In the HAM solution, there exists an auxiliary parameter ¯h which provides a convenient way to adjust and check the convergence region of the solution series. In the model problems, an appropriate choice of the auxiliary parameter has been examined for increasing values of time

An effective approach to numerical soliton solutions for the Schrödinger equation via modified cubic B-spline differential quadrature method

In this study, an effective differential quadrature method (DQM) which is based on modified cubic B-spline (MCB) has been implemented to obtain the numerical solutions for the nonlinear Schrödinger (NLS) equation. After separating the Schrödinger equation into coupled real value differential equations,we have discretized using DQM and then obtained ordinary differential equation systems. For time integration, low storage strong stability-preserving Runge–Kutta method has been used. Numerical solutions of five different test problems have been obtained. The efficiency and accuracy of the method have been measured by calculating error norms L2 and Linfinity and two lowest invariants I1 and I2. Also relative changes of invariants are given. The newly obtained numerical results have been compared with the published numerical results and a comparison has shown that the MCB-DQM is an effective numerical scheme to solve the nonlinear Schrödinger equation. © 2017 Elsevier Lt

A new perspective for the numerical solutions of the cmKdV equation via modified cubic B-spline differential quadrature method

In the present paper, a novel perspective fundamentally focused on the differential quadrature method using modified cubic B-spline basis functions are going to be applied for obtaining the numerical solutions of the complex modified Korteweg-de Vries (cmKdV) equation. In order to test the effectiveness and efficiency of the present approach, three test problems, that is single solitary wave, interaction of two solitary waves and interaction of three solitary waves will be handled. Furthermore, the maximum error norm L ? will be calculated for single solitary wave solutions to measure the efficiency and the accuracy of the present approach. Meanwhile, the three lowest conservation quantities will be calculated and also used to test the efficiency of the method. In addition to these test tools, relative changes of the invariants will be calculated and presented. In the end of these processes, those newly obtained numerical results will be compared with those of some of the published papers. As a conclusion, it can be said that the present approach is an effective and efficient one for solving the cmKdV equation and can also be used for numerical solutions of other problems. © 2018 World Scientific Publishing Company

Approximate Analytical Solution to Time-Fractional Damped Burger and Cahn-Allen Equations

The aim of the present paper is to obtain the approximate analytical solutions of time-fractional damped burger and Cahn- Allen equations by means of the homotopy analysis method (HAM). In the HAM solution, there exists an auxiliary parameter ¯h which provides a convenient way to adjust and check the convergence region of the solution series. In the model problems, an appropriate choice of the auxiliary parameter has been examined for increasing values of time

Numerical solution of the complex modified Korteweg-de Vries equation by DQM

Eskisehir Osmangazi University (ESOGU);Eskisehir Tepebasi Municipality;Scientific and Technological Research Council of Turkey (TUBITAK) under the project number 113F226International Conference on Quantum Science and Applications, ICQSA 2016 -- 25 May 2016 through 27 May 2016 -- -- 124644In this paper, a method based on the differential quadrature method with quintic B- spline has been applied to simulate the solitary wave solution of the complex modified Korteweg- de Vries equation (CMKdV). Three test problems, namely single solitary wave, interaction of two solitary waves and interaction of three solitary waves have been investigated. The efficiency and accuracy of the method have been measured by calculating maximum error norm L? for single solitary waves having analytical solutions. Also, the three lowest conserved quantities and obtained numerical results have been compared with some of the published numerical results