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Advances in Applied Mathematics and Mechanics 2022年第5期14卷 1138-1160页

作者： Nur Inshirah Naqiah Ismail zanariah abdul majid Norazak Senu Institute for Mathematical Research Universiti Putra Malaysia43400 UPM SerdangSelangorMalaysia Department of Mathematics and Statistics Faculty of ScienceUniversiti Putra Malaysia43400 UPM SerdangSelangorMalaysia

Neutral Delay Differential Equation(NDDE)is a differential problem that has regularly existed in numerous occurrences and has represented a significant role in dealing with real-life phenomena,especially on their application in biological and physiological processes.A fifth-order two-point hybrid implicit multistep block method(2PIH5)has been formulated in this research for the numerical solution of Neutral Delay Differential Equation(NDDE).A Taylor series interpolation polynomial has been implemented in the formulation of the proposed *** order,consistency,and zero-stability for 2PIH5 have been *** analyses of convergence and stability test have been performed and *** initial value problems for the first-order NDDE with constant or proportional delay have been solved using the proposed block *** numerical results for the proposed method have been presented to prove the adaptability and applicability of the proposed method in solving *** proposed method is proved to be comparable with the other existing *** is assumed to be reliable and efficient for solving the first-order NDDE with constant or proportional delay.

关键词： Constant delay hybrid method multistep block method neutral delay differential equation proportional delay

Two-Point Block Method in Variable Stepsize Technique for Solving Delay Differential Equations

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材料科学与工程（中英文版） 2010年第12期4卷 86-90页

作者： Fuziyah Ishak zanariah abdul majid1 Mohamed Suleiman Faculty of Computer and Mathematical Sciences Universiti Teknologi MARA Shah Alam 40450 Malaysia Department of Mathematics Universiti Putra Malaysia Serdang 43400 Malaysia

New Painlevé Integrable(3+1)-Dimensional Combined pKP–BKP Equation:Lump and Multiple Soliton Solutions

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Chinese Physics Letters 2023年第12期40卷 19-26页

作者： abdul-majid Wazwaz Department of Mathematics Saint Xavier UniversityChicagoIL 60655USA

We introduce a new form of the Painlevé integrable(3+1)-dimensional combined potential Kadomtsev–Petviashvili equation incorporating the B-type Kadomtsev–Petviashvili equation(pKP–BKP equation). We perform the Painlevé analysis to emphasize the complete integrability of this new(3+1)-dimensional combined integrable equation. We formally derive multiple soliton solutions via employing the simplified Hirota bilinear method. Moreover, a variety of lump solutions are determined. We also develop two new(3+1)-dimensional pKP–BKP equations via deleting some terms from the original form of the combined p KP–BKP equation. We emphasize the Painlevé integrability of the newly developed equations, where multiple soliton solutions and lump solutions are derived as well. The derived solutions for all examined models are all depicted through Maple software.

关键词： equation method integrable

A New Integrable (2+1)-Dimensional Generalized Breaking Soliton Equation:N-Soliton Solutions and Traveling Wave Solutions

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Communications in Theoretical Physics 2016年第10期65卷 385-388页

作者： abdul-majid Wazwaz Department of Mathematics Saint Xavier University

In this work,we study a new(2+1)-dimensional generalized breaking soliton equation which admits the Painleve property for one special set of *** derive multiple soliton solutions,traveling wave solutions,and periodic ... 详细信息

关键词： breaking soliton equations Hirota bilinear method multiple soliton solutions traveling wave solutions

Vertex Cover Optimization Using a Novel Graph Decomposition Approach

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Computers, Materials & Continua 2022年第10期73卷 701-717页

作者： abdul Manan Shahida Bashir abdul majid Department of Mathematics University of GujratGujrat50700Pakistan Department of Physics University of GujratGujrat50700Pakistan

The minimum vertex cover problem(MVCP)is a well-known combinatorial optimization problem of graph *** MVCP is an NP(nondeterministic polynomial)complete problem and it has an exponential growing complexity with respect to the size of a *** algorithm exits till date that can exactly solve the problem in a deterministic polynomial time ***,several algorithms are proposed that solve the problem approximately in a short polynomial time *** algorithms are useful for large size graphs,for which exact solution of MVCP is impossible with current computational *** MVCP has a wide range of applications in the fields like bioinformatics,biochemistry,circuit design,electrical engineering,data aggregation,networking,internet traffic monitoring,pattern recognition,marketing and franchising *** work aims to solve the MVCP approximately by a novel graph decomposition *** decomposition of the graph yields a subgraph that contains edges shared by triangular edge structures.A subgraph is covered to yield a subgraph that forms one or more Hamiltonian cycles or *** order to reduce complexity of the algorithm a new strategy is also *** reduction strategy can be used for any algorithm solving *** on the graph decomposition and the reduction strategy,two algorithms are formulated to approximately solve the *** algorithms are tested using well known standard benchmark *** key feature of the results is a good approximate error ratio and improvement in optimum vertex cover values for few graphs.

关键词： Combinatorial optimization graph theory minimum vertex cover problem maximum independent set maximum degree greedy approach approximation algorithms benchmark instances

Perturbation,symmetry analysis,Bäcklund and reciprocal transformation for the extended Boussinesq equation in fluid mechanics

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Communications in Theoretical Physics 2021年第4期73卷 21-28页

作者： Gangwei Wang abdul-majid Wazwaz School of Mathematics and Statistics Hebei University of Economics and BusinessShijiazhuang050061China Department of Mathematics Saint Xavier UniversityChicagoIL 60655United States of America

In this work,we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics,scientific fields,and ocean *** equation will be reduced to the Korteweg-de Vries equation via using the perturbation *** derive the corresponding vectors,symmetry reduction and explicit solutions for this *** readily obtain Bäcklund transformation associated with truncated Painlevé*** also examine the related conservation laws of this equation via using the multiplier ***,we investigate the reciprocal Bäcklund transformations of the derived conservation laws for the first time.

关键词： Boussinesq equation perturbation and symmetry analysis Bäcklund transformation conservation laws

A review on first principles based studies for improvement of cathode material of lithium ion batteries

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Journal of Energy Chemistry 2018年第1期27卷 219-237页

作者： Arslan Ullah abdul majid Naema Rani Department of Physics.University of Cujrat.50700 Gujrat Pakistan Office of Research Innovation and CommercializationUniversity of GujratGujratPakistan

Lithium ion batteries（LIBs） are currently best energy storage devices providing rechargeable electrical storage to wide variety of applications – from portable electronics to automobiles. Though, these batteries are fully adopted, widely used and commercialized, but researchers are still extensively working on their constituent materials and developing technology to improve their performance. A major part of related research activities is devoted to the electrode of the battery for improvement in its performance thereby addressing issues like safety, lifetime, specific capacity, energy density and most importantly abundance and cost. There are number of cathode materials that have been proposed and tested at laboratory scale and subsequently utilized in commercialized batteries ever since the appearance of LIBs. Owing to the availability of improved computational resources in the last decade, first principles calculation has become a reliable tool and played a vital role to predict the material properties of electrodes prior to their experimental analysis. This review gives a comprehensive insight and thorough analysis of the global research efforts related to the cathode materials based on first principles framework, sheds light on current status of knowledge and explores the ways forward.

关键词： Lithium ion batteries Electrodes First principles methods

Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves

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Chinese Physics B 2023年第4期32卷 226-236页

作者：赵忠龙和玲超 abdul-majid Wazwaz School of Mathematics North University of ChinaTaiyuan 030051China College of Mathematics Taiyuan University of TechnologyTaiyuan 030024China Department of Mathematics Saint Xavier UniversityChicagoIL 60655USA

A large member of lump chain solutions of the(2+1)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili(BKP)equation are constructed by means of theτ-function in the form of *** lump chains are formed by periodic arrangement of individual lumps and travel with distinct group and *** analytical method related dominant regions of polygon is developed to analyze the interaction dynamics of the multiple lump *** degenerate structures of parallel,superimposed,and molecular lump chains are *** interaction solutions between lump chains and kink-solitons are investigated,where the kink-solitons lie on the boundaries of dominant region determined by the constant term in theτ-***,the hybrid solutions consisting of lump chains and individual lumps controlled by the parameter with high rank and depth are *** analytical method presented in this paper can be further extended to other integrable systems to explore complex wave structures.

关键词： lump chains interaction solutions BKP equation

The simplified Hirota’s method for studying three extended higher-order KdV-type equations

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Journal of Ocean Engineering and Science 2016年第3期1卷 181-185页

作者： abdul-majid Wazwaz Department of Mathematics Saint Xavier UniversityChicagoIL 60655USA

In this work we study three extended higher-order KdV-type *** Lax-type equation,the Sawada-Kotera-type equation and the CDG-type equation are derived from the extended KdV *** use the simplified Hirota’s direct method to derive multiple soliton solutions for each *** show that each model gives multiple soliton solutions,where the structures of the obtained solutions differ from the solutions of the canonical form of these equations.

关键词： Fifth-order KdV equation Hirota’s method Dispersion relation

A new integrable nonlocal modified KdV equation:Abundant solutions with distinct physical structures

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Journal of Ocean Engineering and Science 2017年第1期2卷 1-4页

作者： abdul-majid Wazwaz Department of Mathematics Saint Xavier UniversityChicagoIL 60655United States

In this work we study a new integrable nonlocal modified Korteweg-de Vries equation(mKdV)which arises from a reduction of the AKNS scattering *** use a variety of distinct techniques to determine abundant solutions with distinct physical *** show that this nonlocal equation possesses a family of traveling solitary wave solutions that include solitons,kinks,periodic and singular solutions.

关键词： Nonlocal modified KdV equation Soliton solutions Periodic solutions Exponential solutions