
Mehnaz ShakeelWomen University Mardan
Mehnaz Shakeel
Doctor of Philosophy
About
15
Publications
1,755
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Publications
Publications (15)
In this article, radial basis function collocation scheme is adopted for the numerical solution of fractional partial differential equations. This method is highly demanding because of its meshless nature and ease of implementation in high dimensions and complex geometries. Time derivative is approximated by Caputo derivative for the values of α∈0,...
This paper is concerned with the numerical solution of timefractional partial differential equations (PDEs) via local meshless differential
quadrature collocation method (LMM) using radial basis functions (RBFs). For the sake of comparison, global version of the meshless method is also considered. The meshless methods do not need mesh and approxima...
In this study, the interaction of counter-propagating ion acoustic shock waves in three-component unmagnetized plasmas with inertial warm ions, superthermal electrons and positrons are examined. By employing the extended Poincare-Lighthill-Kuo (PLK) method, two-sided Korteweg-deVries-Burgers (KdVB) equations and their corresponding phase shifts for...
This article discusses the use of self-similar symmetry to analyze static plane symmetric spacetime. A computer algorithm is employed to convert the symmetry equations, resulting in a tree structure known as a Riff tree, which is utilized for analyzing the aforementioned symmetry within the specified spacetime. The tree comprises several pivots and...
In this study, we use the Rif tree approach to explore self-similar vector fields in Bianchi type III spacetime. This work adopt a computer-based method to transform symmetry equations into an involutive form that is simplified and divides the integration problem into multiple cases, each represented as a tree structure. In some cases, the metric f...
This study examines entropy generation in the peristaltic flow of Johnson–Segalman fluid through a curved channel, considering the effects of Hall and ion slip due to an externally applied magnetic field and activation energy. The fluid dynamics are modeled using a highly nonlinear mathematical framework, which is non‐dimensionalized and simplified...
In this study, we present two meshless schemes, namely the radial basis function (RBF) method and the polynomial method, for the numerical investigation of the time-fractional Harry Dym equation and the Drinfeld-Sokolov-Wilson system. In both methods, the temporal derivatives are estimated using the Caputo operator, while the spatial derivatives ar...
In this manuscript, a hybrid numerical technique is presented for solving three-dimensional hyperbolic
telegraph equations. The proposed technique is based on the Haar wavelet collocation method and the
finite difference method. In this technique, the space derivatives are estimated by truncated Haar wavelet
series, while the time derivatives are a...
Rici collineations (RCs) have been used in this research to study the locally rotationally symmetric (LRS) Bianchi type I spacetimes. To accomplish our objectives, the RC equations are typically integrated for both situations of the Ricci tensor, degenerate and non-degenerate. Throughout this work, a number of situations occur that provide various...
The basic aim of this research is to investigate the main features of the peristaltic flow of Johnson-Segalman fluid in a curved flow channel in the presence of a homogeneous-heterogeneous reaction. The fluid is considered electrically conducting with a radial magnetic field effect. The constitutive relation for energy is formulated with the additi...
In this article, a hybrid numerical method based on Haar wavelets and finite difference method is proposed for the solution of hyperbolic telegraph interface model in one spacial dimension. We considered the problems having both constant and variable coefficients around interfaces of discontinuity across a fixed interface. In this method, the highe...
In this work, radial basis function collocation method (RBFCM) is implemented
for generalized time fractional Gardner equation (GTFGE). The RBFCM is
meshless and easy-to-implement in complex geometries and higher dimensions,
therefore, it is highly demanding. In this work, the Caputo derivative of
fractional order ξ ∈ (0, 1] is used to approximate...
In this work, numerical solution of multi term space fractional PDE is
calculated by using radial basis functions. The fractional derivatives of
radial basis functions are evaluated by Caputo and Riemann-Liouville
definitions. Local radial basis functions are applied to get stable and
accurate solution the problem. Accuracy of the method is assesse...
In this study, the meshless collocation approach is used to determine the
numerical solution the generalized time-fractional Gardner equation. The
Crank-Nicolson technique is used to approximate space derivatives, whereas
the Caputo derivative of fractional order is used to approximate the first
order time fractional derivative. The numerical solut...
Questions
Question (1)
Most common question about fractional derivative is that "What is its physical interpretation?" As first order derivative refers to the velocity of the displacement while the second derivative is for the acceleration but what about the 0.5 order derivative of displacement?