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Adoption of Homotopy Perturbation Method (HPM) for non-Darcy Flow in Porous Media
For non-Darcy flow in coarse porous media, an analytical solution based on the Homotopy Perturbation Method (HPM) is proposed. Subsurface water...
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An optimal and modified homotopy perturbation method for strongly nonlinear differential equations
Homotopy perturbation method (HPM) is one of the most popular semi-analytical methods to solve a nonlinear differential equation. However, in HPM,...
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Topological 3D Spatial Interpolation Based on the Interval-Valued Homotopy Continuation
Estimating unknown values using its surrounding measured values is called spatial interpolation, a vital tool for estimating continuous spatial data...
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Homotopy Analysis Method
In this entry, we describe the basic ideas of the homotopy analysis method (HAM), an analytic approach to get convergent series solutions of strongly...
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A Novel Mathematical Model and Homotopy Perturbation Method Analyzing the Effects of Saturated Incidence and Treatment Rate on COVID-19 Eradication
Saturated incidence rates and treatment responses are essential in epidemiology and clinical research. They signify peak event occurrences in a...
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A Homotopy Continuation Solution of the Covariance Extension Equation
Algebraic geometry plays an important role in the theory of linear systems for (at least) three reasons. First, the Laplace transform turns...
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Variable Speed Wind Turbine Control Using the Homotopy Perturbation Method
In this study, we present a method to obtain optimal control of the variable-speed fixed-pitch wind turbine using the homotopy perturbation method...
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Improved Homotopy Perturbation Solution for Nonlinear Transverse Vibration of Orthotropic Membrane
ObjectiveDue to its characteristics of being light and flexible, membrane has been widely used in long-span stadiums and other buildings. However,...
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Numerical Solution of Eighth Order Boundary Value Problems by Using Vieta-Lucas Polynomials
In this paper, the eighth order boundary value problems (BVPs) are solved by utilizing the Vieta-Lucas polynomials based scheme. The operational...
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Static analysis of composite beams on variable stiffness elastic foundations by the Homotopy Analysis Method
New analytical solutions for the static deflection of anisotropic composite beams resting on variable stiffness elastic foundations are obtained by...
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A Reliable Numerical Approach for Liouville-Caputo Time-fractional Belousov-Zhabotinsky Equation Arising in Chemical Oscillatory Reaction
This paper suggests a computationally effective homotopy perturbation Sumudu transform technique (HPSTT) to investigate various time-fractional...
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An approach to solving the forward kinematics of the 5-RPUR (3T2R) parallel manipulator
This work is devoted to simplifying the formulation and solution of the closure equations associated with the forward kinematic problem (FKP) of the...
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Thermal Performance Evaluation of Longitudinal Fins with Various Profiles Using Homotopy Perturbation Method
The thermal performance of longitudinal radiative–convective fins with rectangular, trapezoidal, and concave parabolic profiles was analyzed by the...
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A new computational method-based integral transform for solving time-fractional equation arises in electromagnetic waves
In this paper, the He–Elzaki transform method (HEM) is proposed. The method is formulated by combining He’s variation iteration method and the...
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Homotopy Analysis Method
In this entry, we describe the basic ideas of the homotopy analysis method (HAM), an analytic approach to get convergent series solutions of strongly...
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A spectral shifted gegenbauer collocation method for fractional pantograph partial differential equations and its error analysis
This study presents a new numerical approach for solving fractional-order pantograph partial-differential equations, in which the fractional...
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A toric deformation method for solving Kuramoto equations on cycle networks
The study of frequency synchronization configurations in Kuramoto models for networks of coupled oscillators is a ubiquitous mathematical problem...
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Approximate Numerical Solution of the Nonlinear Klein-Gordon Equation with Caputo-Fabrizio Fractional Operator
This work analyze the linear and nonlinear fractional Klein-Gordon equation using fractional homotopy perturbation transform method (FHPTM) via...
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Integer Algorithm: A Useful Tool for Fault Diagnosis of Analog Circuits
This paper presents an efficient numerical method to solve systems of nonlinear algebraic equations. The method uses a homotopy simplicial approach...
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A GPU Homotopy Path Tracker and End Game for Mechanism Synthesis
This paper presents an implementation of a path tracking algorithm and end game for the homotopy solution of mechanism synthesis equations using a...