B-Spline collocation method for numerical solution of nonlinear kawahara and modified kawahara equations

In this paper, a collocation method is applied for solving the Kawahara and modified Kawahara equations. For the spatial discretization, we use the sextic B-spline collocation (SBSC) method on uniform meshes, finite difference scheme is employed for the time discretization. The stability analysis of the collocation methods are examined by the Von Neumann approach. Numerical results demonstrate the efficiency and accuracy of the proposed methods.Publisher's Versio

Error estimate and adaptive refinement in mixed discrete least squares meshless method

The node moving and multistage node enrichment adaptive refinement procedures are extended in mixed discrete least squares meshless (MDLSM) method for efficient analysis of elasticity problems. In the formulation of MDLSM method, mixed formulation is accepted to avoid second-order differentiation of shape functions and to obtain displacements and stresses simultaneously. In the refinement procedures, a robust error estimator based on the value of the least square residuals functional of the governing differential equations and its boundaries at nodal points is used which is inherently available from the MDLSM formulation and can efficiently identify the zones with higher numerical errors. The results are compared with the refinement procedures in the irreducible formulation of discrete least squares meshless (DLSM) method and show the accuracy and efficiency of the proposed procedures. Also, the comparison of the error norms and convergence rate show the fidelity of the proposed adaptive refinement procedures in the MDLSM method

Deviation of the Error Estimation for Second Order Fredholm-Volterra Integro Differential Equations

In this paper we study the deviation of the error estimation for the second order Fredholm-Volterra integro-differential equations. We prove that for m degree piecewise polynomial collocation method, our method provides O(hm+1) as the order of the deviation of the error. Also numerical results in the final section are included to confirm the theoretical results

Application of goal-oriented error estimation and adaptive mesh refinement on thermo-mechanical multifield problems

Application of goal-oriented error estimation and adaptive mesh re_nement on thermo-mechanical multi_eld problem

Error Estimate and Adaptive Refinement in Mixed Discrete Least Squares Meshless Method

The node moving and multistage node enrichment adaptive refinement procedures are extended in mixed discrete least squares meshless (MDLSM) method for efficient analysis of elasticity problems. In the formulation of MDLSM method, mixed formulation is accepted to avoid second-order differentiation of shape functions and to obtain displacements and stresses simultaneously. In the refinement procedures, a robust error estimator based on the value of the least square residuals functional of the governing differential equations and its boundaries at nodal points is used which is inherently available from the MDLSM formulation and can efficiently identify the zones with higher numerical errors. The results are compared with the refinement procedures in the irreducible formulation of discrete least squares meshless (DLSM) method and show the accuracy and efficiency of the proposed procedures. Also, the comparison of the error norms and convergence rate show the fidelity of the proposed adaptive refinement procedures in the MDLSM method

Knowledge and attitude toward AIDS among people admitted to the Qazvin faculty of Dentistry (2014)

Background: AIDS is as a global fatal disease and the only way to combat the disease is education and knowledge about the methods of transmission and prevent of the disease. Objective: The aim of this study was to evaluate the knowledge and attitudes of people admitted to the Qazvin faculty of Dentistry toward AIDS. Methods: A cross-sectional descriptive study was conducted in 2013-2014 using a standard questionnaire between 270 people admitted to the Qazvin faculty of Dentistry. Findings: According to data analysis, 150 subjects (55.6%) had a poor knowledge about the disease and with increasing the age, knowledge was lower. The attitude of 153 subjects (56.7%) was moderate. All the participants were married and had 20 years old at least. Conclusion: This study indicated that the knowledge and attitude of people admitted to the Qazvin faculty of Dentistry was inappropriate and there was a necessity to promote absolute knowledge and good attitude about AIDS

A stochastic computational method based on goal-oriented error estimation for heterogeneous geological materials

A stochastic computational method based on goal-oriented error estimation for heterogeneous geological material

MAS and PFG NMR studies of proton exchanges membranes for electrolytic water splitting

Proton exchange membranes (PEMs) are a critical component in acidic water electrolyzers. They serve the purpose of separating cathode and anode compartments and thus preventing a loss in faradaic efficiency, while simultaneously providing a high proton conductivity for charge compensation. In order to minimize the ohmic losses during electrolysis, the electrode material is often coated directly onto the PEM in order to create a membrane-electrode-assembly (MEA) [1].While high ionic conductivity and impermeability for electrolysis products are crucial properties of a PEM, long-term stability and resistance to chemical and structural alteration are a decisive factor for their industrial application. It is assumed that losses in the stability of the polymer occur due to the formation and attack of radicals on the polymer backbone and the side chains. In particular, the polar side chains are responsible for the formation of hydrophilic channels inside the polymer which promote the proton transport of the material. The Fenton reaction, where iron cations react with peroxide formed during electrolysis, is discussed to be a main mechanism of radical formation [2].Nuclear magnetic resonance (NMR) spectroscopy has been established as a powerful tool for the investigation of polymers and especially ionomers. In this study, magic angle spinning (MAS) and pulsed field gradient (PFG) NMR techniques has been applied for the investigation of the Fenton reaction in short-side-chained PEM materials. The PEMs were treated in a Fenton reagent, i.e. an aqueous solution of Fe(ii) and H2O2. In addition, the PEMs were treated in an aqueous iron(ii) solution as a reference experiment. The effect of Fenton degradation on the chemical structure and chain mobility was studied using MAS NMR experiments, and changes in proton transport properties were assessed by PFG NMR. It was shown that radicals preferentially attack the side chains of the PEM polymer, which decreases the overall mobility of the polar groups and thus affects proton mobility.We thankfully acknowledge funding and support by the Bundesministerium für Bildung und Forschung (BMBF). [1] S. Shiva Kumar et al., Materials Science for Energy Technologies, 2. 442-454, 2019.[2] L. Ghassemzadeh et al., Journal of Power Sources, 196, 2490-2497, 2011