Least Square Homotopy Perturbation Method for Ordinary Differential Equations

Qayyum, Mubashir; Oscar, Imbsat

doi:10.1155/2021/7059194

Cited by 7 publications

(9 citation statements)

References 24 publications

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“…On the contrary, the system of the peripheral region cannot be solved exactly, so we adopted the scheme of perturbation (HPM) [46][47][48] in which the same linear operator is chosen for velocity, heat, and energy functions, i.e., H � z 2 /zr 2 + 1/rz/zr. After using the routine calculation of HPM, the final solutions have been composed in subsequent forms:…”

Section: Solution Methodsmentioning

confidence: 99%

Flow Analysis of Two-Layer Nano/Johnson–Segalman Fluid in a Blood Vessel-like Tube with Complex Peristaltic Wave

Zeeshan

Riaz

Alzahrani

et al. 2022

Mathematical Problems in Engineering

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Biologically inspired micropumps using the phenomena of peristalsis are highly involved in targeted drugging in pharmacological engineering. This study analyzed theoretically the transport of two immiscible fluids in a long flexible tube. The core region contains Johnson–Segalman non-Newtonian fluid, while the peripheral region is saturated by nanofluid. It is assumed that Darcy’s porous medium is encountered close to the walls of the tube. A complex peristaltic wave is transmitted on the compliant wall which induces the flow. Equations of continuity, momentum, energy, and nanoparticle concentration are used in modelling the problem. The modelled problem for both the regions, i.e., core and peripheral regions are developed with the assumptions of long wavelength and creeping flow. Temperature, velocity, and shear stress at the interface are assumed to be equal. The system of equations is solved analytically. The graphical results for different involving parameters are displayed and thoroughly discussed. It is received that the heat transfer goes inverse with fluid viscosity in the peripheral region, but opposite measurements are obtained in the core region. This theoretical model may be considerable in some medical mechanisms such as targeted drug delivery, differential diagnosis, and hyperthermia. Moreover, no study on non-Newtonian nanofluid is reported yet for the two-layered flow system, so this study will give a good addition in the literature of biomedical research.

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Section: Solution Methodsmentioning

confidence: 99%

Flow Analysis of Two-Layer Nano/Johnson–Segalman Fluid in a Blood Vessel-like Tube with Complex Peristaltic Wave

Zeeshan

Riaz

Alzahrani

et al. 2022

Mathematical Problems in Engineering

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“…In Table 3, we report the absolute error difference between the exact analytical solution and, the proposed solution E EDSM and, further validated with E SRKM4 and the other methods described in [23].…”

Section: Numerical Examplesmentioning

confidence: 97%

Efficient Decomposition Shooting Method for Solving Third-Order Boundary Value Problems

Al-Zaid,

Alzahrani,

Bakodah

et al. 2023

IJMNTA

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The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and, the modified shooting method. A complete derivation of the proposed method has been provided, in addition to its numerical implementation and, validation via the utilization of the Runge-Kutta method and, other existing methods. The method has been applied to diverse test problems and turned out to perform remarkably. Lastly, the simulated numerical results have been graphically illustrated and, also supported by some absolute error comparison tables.

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“…These methods are of great interest for the scientific community to accurately explore and predict different situations. Few of these methods include Adomian decomposition method (ADM) and its different modifications [9], variation iterative method (VIM) [10], HPM and its various modifications [11,12,13,14,15], residual power series method (RPSM) [16], and Block-Pulse functions method with operational matrix [17].…”

Section: Introductionmentioning

confidence: 99%

Modification of Homotopy Perturbation Algorithm Through Least Square Optimizer for Higher Order Integro-Differential Equations

Qayyum

Oscar

2023

Punjab Univ. j. math.

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In this manuscript, modification of homotopy perturbation method (HPM) is proposed for integro-differential equations by coupling the least square method (LSM) with HPM. Improved accuracy in a very few iterations is the general advantage of this technique. The proposed method is applied to different higher order integro-differential equations of linear and nonlinear nature, and results are compared with exact as well as available solutions from the literature. Numerical and graphical analysis reveal that the proposed algorithm is reliable for integro-differential equations and hence can be utilized for more complex problems.

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Least Square Homotopy Perturbation Method for Ordinary Differential Equations

Cited by 7 publications

References 24 publications

Flow Analysis of Two-Layer Nano/Johnson–Segalman Fluid in a Blood Vessel-like Tube with Complex Peristaltic Wave

Flow Analysis of Two-Layer Nano/Johnson–Segalman Fluid in a Blood Vessel-like Tube with Complex Peristaltic Wave

Efficient Decomposition Shooting Method for Solving Third-Order Boundary Value Problems

Modification of Homotopy Perturbation Algorithm Through Least Square Optimizer for Higher Order Integro-Differential Equations

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