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Numerical Solution of the Three-Dimensional Helmholtz Equation

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Chinese Physics Letters 2010年第6期27卷 1-4页

作者： syed tauseef mohyud-din Ahmet Ylldlrim Department of Basic Sciences HITEC University Taxila Cantt Pakistan Department of Mathematics Ege University 35100 Bornova-izmir Turkey

We apply the homotopy analysis method to solve the nonhomogeneous multidimensional partial differential equation model problem. The analytic solutions are calculated in terms of convergent series with easily computable components. The nonhomogeneous problem is quickly solved by observing the self-canceling ＂noise＂ terms whose sum vanishes in the limit. Numerical results clearly reveal the complete reliability and efficiency of the proposed algorithm.

关键词： Computers Solution Helmholtz Equation

Poincaré-MacMillan Equations of Motion for a Nonlinear Nonholonomic Dynamical System

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Chinese Physics Letters 2012年第3期29卷 132-134页

作者： Amjad Hussain syed tauseef mohyud-din Ahmet Yildirim Department of Mathematics Zhejiang UniversityHangzhou 310027 Department of Mathematics HITEC UniversityTaxila Cantt Pakistan Department of Mathematics Ege University35100 Bornova IzmirTurkey University of South Florida Department of Mathematics and StatisticsTampaFL 33620-5700USA

MacMillan's equations are extended to Poincaré's formalism,and MacMillan's equations for nonlinear nonholonomic systems are obtained in terms of Poincaré*** equivalence of the results obtained here with other forms ... 详细信息

关键词： Poincaré parameters MacMillan

Analytical and Numerical Approaches to Squeezing Flow and Heat Transfer between Two Parallel Disks with Velocity Slip and Temperature Jump

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Chinese Physics Letters 2012年第11期29卷 152-156页

作者： Amjad Hussain syed tauseef mohyud-din Taqi Ahmed Cheema Department of Mathematics Zhejiang UniversityHangzhou 310027 Department of Mathematics HITEC UniversityTaxila CantPakistan School of Mechanical Engineering Kyungpook National University1370 Sankyuk-dongBuk-guDeagu702-701Korea

Analytic and numerical techniques are presented to analyze the influence of temperature and wall slip conditions on the unsteady flow and heat transfer via viscous fluid squeezed between two parallel disks in the presence of an applied magnetic *** governing partial differential equations for momentum and heat transfer are reduced to a system of coupled nonlinear ordinary differential equations using similarity *** homotopy analysis method(HAM)is then utilized to find explicit series solution of the resulting *** convergence of the obtained solution is carefully *** check the reliability of the method the same problem is also solved by using the shooting method and an excellent agreement is observed between the two sets of *** of various parameters of practical importance on the velocity and temperature profiles is studied and portrayed *** of skin friction coefficient and local Nusselt number are tabulated by assigning different values to various emerging parameters.

关键词： field ordinary unsteady

On analytical solution of system of nonlinear fractional boundary value problems associated with obstacle

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Journal of Ocean Engineering and Science 2018年第1期3卷 49-55页

作者： Asif Waheed syed tauseef mohyud-din Iqra Naz Department of Mathematics COMSATS Institute of Information TechnologyAttockPakistan Center for Research(CFR) University of Islamabad(UoI)IslamabadPakistan

In this paper,we use the modified variation of parameters method(MVPM),an elegant coupling of variation of parameters method(VPM)and Adomian’s decomposition method(ADM),for finding the analytical solution of system of nonlinear fractional boundary value problems associated with *** sense of fractional derivative is used to coup up with fractional *** results are calculated in terms of series with easily computable *** used technique is quite easy and convenient for such type problems because it has been previously applied over several nonlinear obstacle systems.

关键词： Modified variation of parameters method Caputo sense of fractional derivative System of nonlinear fractional boundary value problems

Investigating biological population model using exp-function method

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International Journal of Biomathematics 2016年第2期9卷 159-173页

作者： Qazi Mahmood Ul Hassan syed tauseef mohyud-din Department of Mathematics Faculty of Sciences HITEC University Taxila 47080 Pakistan

This paper is the spectator of the arrangement of an efficient transformation and exp-function technique to build up generalized exact solutions of the biological population model equation. Computational work and subsequent numerical results re-identify the effectiveness of proposed algorithm. It is pragmatic that recommended plan is greatly consistent and may be comprehensive to other nonlinear differential equations of fractional order.

关键词：生物种群模型函数法非线性微分方程模型方程广义解分数阶

A novel (G'/G)-expansion method and its application to the Boussinesq equation

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Chinese Physics B 2014年第2期23卷 34-43页

作者： Md.Nur Alam Md.Ali Akbar syed tauseef mohyud-din Department of Mathematics Pabna University of Science and Technology Department of Applied Mathematics University of Rajshahi Department of Mathematics HITEC UniversityTaxila Cantt

In this article, a novel （G＇/G）-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant traveling wave solutions involving parameters to the Boussinesq equation by means of the suggested method. The performance of the method is reliable and useful, and gives more general exact solutions than the existing methods. The new （G＇/G）-expansion method provides not only more general forms of solutions but also cuspon, peakon, soliton, and periodic waves.

关键词： (G'/G)-expansion method Boussinesq equation solitary wave solutions auxiliary nonlinear ordinary differential equation

On biological population model of fractional order

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International Journal of Biomathematics 2016年第5期9卷 107-119页

作者： syed tauseef mohyud-din Ayyaz Ali Bandar Bin-Mohsin Department of Mathematics HITEC University Taxila Pakistan Department of Mathematics College of Sciences King Saud University Riyadh Saudi Arabia

In this paper, we extensively studied a mathematical model of biology. It helps us to understand the dynamical procedure of population changes in biological population model and provides valuable predictions. In this model, we establish a variety of exact solutions. To study the exact solutions, we used a fractional complex transform to convert the particular partial differential equation of fractional order into corresponding partial differential equation and modified exp-function method is implemented to investigate the nonlinear equation. Graphical demonstrations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, unfailing, well-organized and pragmatic for fractional PDEs and could be protracted to further physical happenings.

关键词：生物种群模型分数阶偏微分方程非线性方程数学模型人口变化图形演示 PDEs

Ma’s Variation of Parameters Method for Fisher’s Equations

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Advances in Applied Mathematics and Mechanics 2010年第3期2卷 379-388页

作者： syed tauseef mohyud-din Ahmet Yıldırım HITEC University Taxila Cantt Pakistan Ege University Department of Mathematics35100 Bornova-IzmirTurkey

In this paper,we apply Ma’s variation of parameters method(VPM)for solving Fisher’s *** suggested algorithm proved to be very efficient and finds the solution without any discretization,linearization,perturbation or... 详细信息

关键词： Variation of parameters method variational iteration method nonlinear problems Fisher’s equation nonlinear diffusion equation error estimates

A conformable mathematical model for alcohol consumption in Spain

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International Journal of Biomathematics 2019年第5期12卷 203-219页

作者： Aqsa Nazir Naveed Ahmed Umar Khan syed tauseef mohyud-din Pepartment of Mathefnaticst Faculty of HITEC University Taxila CanttPakistan Department of Mathematics and Statistics Hazara University MansehruPakistan

A study on the conformable model of alcohol consumption in Spain has been *** the proposed model,the existence as well as the uniqueness of the solution has been discussed with the help of fixed-point *** analytical technique,Variational Iteration Method (VIM),has been used to obtain the solution to the governing system of differential *** the help of suitable plots,the role of fractional order derivative has been *** decreasing values of fractional order derivative,decrease in the number of non-consumers and non-risk consumers has been *** increasing the value of fractional order derivative,a sharp decrease can be seen in the compartment of *** agreement between the current study and the already existing studies,with ordinary derivatives,has also been pointed out.

关键词： Alcohol consumption nonlinear differential equations initial value problem conformable derivative uniqueness fixed-point postulate VIM