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Solution of Algebraic Lyapunov Equation on Positive-Definite Hermitian Matrices by Using Extended Hamiltonian Algorithm

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Computers, Materials & Continua 2018年第2期54卷 181-195页

作者： Muhammad Shoaib Arif Mairaj Bibi adnan jhangir Department of Mathematics Air UniversityPAF ComplexE-9IslamabadPakistan Department of Mathematics Comsats Institute of Information TechnologyPark RoadChak-ShahzadIslamabadPakistan Department of Mathematics Comsats Institute of Information TechnologyWah CanttPakistan

This communique is opted to study the approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices.We choose the geodesic distance between􀀀AHX􀀀XA and P as the cost function,and put forward the Extended Hamiltonian algorithm(EHA)and Natural gradient algorithm(NGA)for the solution.Finally,several numerical experiments give you an idea about the effectiveness of the proposed algorithms.We also show the comparison between these two algorithms EHA and NGA.Obtained results are provided and analyzed graphically.We also conclude that the extended Hamiltonian algorithm has better convergence speed than the natural gradient algorithm,whereas the trajectory of the solution matrix is optimal in case of Natural gradient algorithm(NGA)as compared to Extended Hamiltonian Algorithm(EHA).The aim of this paper is to show that the Extended Hamiltonian algorithm(EHA)has superior convergence properties as compared to Natural gradient algorithm(NGA).Upto the best of author’s knowledge,no approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices is found so far in the literature.

关键词： Information geometry algebraic lyapunov equation positive-definite hermitianmatrix manifold natural gradient algorithm extended hamiltonian algorithm

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Numerical Study for Magnetohydrodynamic(MHD)Unsteady Maxwell Nanofluid Flow Impinging on Heated Stretching Sheet

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Computer Modeling in Engineering & Sciences 2022年第11期133卷 303-325页

作者： Muhammad Shoaib Arif Muhammad jhangir Yasir Nawaz Imran Abbas Kamaleldin Abodayeh Asad Ejaz Department of Mathematics and Sciences College of Humanities and SciencesPrince Sultan UniversityRiyadh11586Saudi Arabia Department of Mathematics Air UniversityIslamabad44000Pakistan

The numerous applications of Maxwell Nanofluid Stagnation Point Flow,such as those in production industries,the processing of polymers,compression,power generation,lubrication systems,food manufacturing and air conditioning,among other applications,require further research into the effects of various parameters on flow phenomena.In this paper,a study has been carried out for the heat andmass transfer of Maxwell nanofluid flow over the heated stretching sheet.A mathematical model with constitutive expressions is constructed in partial differential equations(PDEs)through obligatory basic conservation laws.A series of transformations are then used to take the system into an ordinary differential equation(ODE).The boundary conditions(BCs)are also treated similarly for transforming into first-order ordinary differential equations(ODEs).Then these ODEs are computed by using the Shooting Method.The effect of factors on the skin friction coefficient,the local Nusselt number,and the local Sherwood number are explored,and the results are displayed graphically.The obtained results demonstrate that by increasing the values of the Maxwell and slip velocity parameters,velocity deescalates.For investigators tasked with addressing unresolved difficulties in the realm of enclosures used in industry and engineering,we thought this work would serve as a guide.

关键词： Maxwell fluid stagnation point flow heat and mass transfer thermal radiations shooting method

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