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Modified Optimal Homotopy Asymptotic Method For Kdv Family Of Equations, Mubashir Qayyum, Muhammad Faisal, Naveed Imran
Modified Optimal Homotopy Asymptotic Method For Kdv Family Of Equations, Mubashir Qayyum, Muhammad Faisal, Naveed Imran
International Journal of Emerging Multidisciplinaries: Mathematics
In this manuscript a hybrid of optimal homotopy asymptotic method (OHAM) with Daftardar - Jafari (DJ) polynomials has been introduced for time dependent KdV family of equations. Proposed methodology is applied to (1+1) and (2+1) soliton KdV equations and results are compared with classical OHAM. Analysis reveals that proposed modification is an effective way of getting better accuracy with less computational cost, and can be applied to more complex phenomena.
Entropy Analysis For Three-Dimensional Stretched Flow Of Viscous Fluid Engaging Radiation Effect And Double Diffusion Phenomenon, Syed Tehseen Abbas, Muhammad Sohail, Imran Haider
Entropy Analysis For Three-Dimensional Stretched Flow Of Viscous Fluid Engaging Radiation Effect And Double Diffusion Phenomenon, Syed Tehseen Abbas, Muhammad Sohail, Imran Haider
International Journal of Emerging Multidisciplinaries: Mathematics
A useful technique for comprehending the thermodynamic behavior of fluid flows is entropy analysis. In this paper, we explore the involvement and transfer of entropy in a stretched three-dimensional flow of a viscous fluid. The flow is presumed to be both laminar and incompressible, whereas the properties of the fluid are considered to be unchanged. The governing equations: continuity; momentum; and energy equations; are calculated using the necessary boundary conditions. Considering the acquired velocity and temperature profiles, the entropy generation rate and fluxes are calculated. The results demonstrate that entropy production is significantly influenced by the flow's stretching rate. Through …
Homotopy Perturbation Laplace Method For Boundary Value Problems, Mubashir Qayyum, Khadim Hussain
Homotopy Perturbation Laplace Method For Boundary Value Problems, Mubashir Qayyum, Khadim Hussain
International Journal of Emerging Multidisciplinaries: Mathematics
Most of the real situations are typically modeled as differential equations (DEs). Accurate solutions of such equations is one of the objective of researchers for the analysis and predictions in the physical systems. Typically, pure numerical approaches are utilized for the solution of such problems. These methods are usually consistent, but due to discretization and round-off errors, accuracy can be compromised. Also, pure numerical schemes may be computationally expensive and have large memory requirement. Due to this reason, current manuscript proposed a hybrid methodology by combining homotopy perturbation method (HPM) with Laplace transformation. This scheme provides excellent accuracy in less …
Utilization Of Adomain Decomposition Method And Laplace Transform To Study Fractional Kdv And Fractional Benjamin Models Via Caputo Fractional Operator, Muhammad Sohail, Hina Younis
Utilization Of Adomain Decomposition Method And Laplace Transform To Study Fractional Kdv And Fractional Benjamin Models Via Caputo Fractional Operator, Muhammad Sohail, Hina Younis
International Journal of Emerging Multidisciplinaries: Mathematics
In the present study, we implement Adomian decomposition method (ADM) to solve fractional potential Korteweg-de Vries (p-KdV) and Benjamin models. The investigated approach is a hybrid of the Adomian decomposition method and the Laplace transform, and the fractional operator developed by Caputo has been utilized in the present research. In a vast accessible domain, the proposed solution tackle impacts and regulates the gained conclusions. Additionally, it provides a simple technique for determining the point of convergence region of the derived result. To ensure that the LADM is realistic and dependable, mathematical simulations for each equation were run, and the results …
Homotopy Analysis Method Using Jumarie’S Approach For Nonlinear Wave-Like Equations Of Fractional-Order, Naveed Imran, Raja Mehmood Khan, Mubashir Qayyum
Homotopy Analysis Method Using Jumarie’S Approach For Nonlinear Wave-Like Equations Of Fractional-Order, Naveed Imran, Raja Mehmood Khan, Mubashir Qayyum
International Journal of Emerging Multidisciplinaries: Mathematics
In this paper, Homotopy Analysis Method (HAM) using the modified Riemann–Liouville fractional derivative proposed by G. Jumarie is applied to tackle the nonlinear wave like equations of fractional-order. The proposed technique is fully compatible with the complexity of these problems and obtained results are highly encouraging. Numerical results coupled with graphical repetitions explicitly reveal the complete reliability and efficiency of the suggested algorithm.
Computational Study Of Twin Circular Particles Settling In Fluid Using A Fictitious Boundary Approach, Imran Abbas, Kamran Usman
Computational Study Of Twin Circular Particles Settling In Fluid Using A Fictitious Boundary Approach, Imran Abbas, Kamran Usman
International Journal of Emerging Multidisciplinaries: Mathematics
The objective of this study is to examine the performance of two adjacent solid particles as they settle in close nearness, with a focus on comprehending the intricate interactions between the particles and the surrounding fluid during the process of sediment transport. Simulations are conducted with different initial horizontal spacing between particles and Reynolds numbers (Re). The findings of the simulations highlight the impact of the initial spacing between particles and Reynolds numbers (Re) as key factors influencing the ultimate settling velocity and separation distance. In general, when the initial spacing between particles is small and the Reynolds number (Re) …
Reduce Differential Transform Method For Analytical Approximation Of Fractional Delay Differential Equation, Tahir Naseem, Adnan Aurang Zeb, Muhammad Sohail
Reduce Differential Transform Method For Analytical Approximation Of Fractional Delay Differential Equation, Tahir Naseem, Adnan Aurang Zeb, Muhammad Sohail
International Journal of Emerging Multidisciplinaries: Mathematics
The study of an entirely new class of differential equations known as delay differential equations or difference differential equations has resulted from the development and application of automatic control systems (DDEs). Time delays are virtually always present in any system that uses feedback control. Because it takes a finite amount of time to sense information and then react to it, a time delay is required. This exploration was carried out for the solution of fractional delay differential equations by using the reduced differential transform method. The results are presented in a series of form that leads to an exact answer. …
Effects Of Thermal Radiation On Jeffery Hamel Flow For Stretchable Walls Of Newtonian Fluid: Analytical Investigation, Umar Khan, Adnan Abbasi, Naveed Ahmed, Basharat Ullah
Effects Of Thermal Radiation On Jeffery Hamel Flow For Stretchable Walls Of Newtonian Fluid: Analytical Investigation, Umar Khan, Adnan Abbasi, Naveed Ahmed, Basharat Ullah
International Journal of Emerging Multidisciplinaries: Mathematics
A viscous, incompressible fluid flows between two inclined planar walls. The walls are able to extend and decrease in size. By substituting an appropriate dimensionless variable, the dimensional partial differential equations of the flow model can be transformed into nondimensional ordinary differential equations. Solving nondimensional velocity and temperature in the model is made possible by the use of an analytical approach known as Adomian's decomposition (AD). Runge-Kutta techniques of order four are used to calculate numerical solutions to ensure the correctness of the analytical answer. On velocity and temperature, the impact of several dimensionless physical quantities embedded in the flow …
Approximate Solution Of Generalized Modified B-Equation By Optimal Auxiliary Function Method, Aatif Ali, Laiq Zada, Rashid Nawaz
Approximate Solution Of Generalized Modified B-Equation By Optimal Auxiliary Function Method, Aatif Ali, Laiq Zada, Rashid Nawaz
International Journal of Emerging Multidisciplinaries: Mathematics
In this study, the implantation of a new semi-analytical method called the optimal auxiliary function method (OAFM) has been extended to partial differential equations. The adopted method was tested upon for approximate solution of generalized modified b-equation. The first-order numerical solution obtained by OAFM has been compared with the variational homotopy perturbation method (VHPM). The method possesses the auxiliary function and control parameters which can be easily handled during simulation of the nonlinear problem. From the numerical and graphical results, we concluded the method is very effective and easy to implement for the nonlinear PDEs.