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- Title
A Convergent Series Approximation Method for Solving Wave-Like Problems: Introducing a Novel Control Convergence Parameter.
- Authors
Mohammed Fawze, Ahmed A.; Fthee, Anees Abdallah
- Abstract
Problems exhibiting wave-like characteristics pervade a diverse array of physical phenomena, including but not limited to longitudinal vibrations of elastic rods or beams, acoustic problems in fluid flow, electric signal transmission along cables, shock waves, chemical exchange processes in chromatography, sediment transport in rivers, plasma wave behavior, and the propagation of both electric and magnetic fields in the absence of charge and dielectric. This study introduces a novel series solution for wave-like problems, leveraging a newly developed technique within the Homotopy Perturbation Method (HPM). The proposed technique operates in the absence of a need for discretization, linearization, or restrictive assumptions, offering distinct advantages over conventional methods. This new version of HPM is designed to address wave-like problems. The technique rests on the assumption that the required solution can be represented as an infinite series sum. The proposed series demonstrates rapid convergence through the use of a control parameter. Initially, the parameter's scope is determined, followed by the selection of a single value that facilitates convergence. Various examples were applied using this technique, yielding satisfactory results. The novel version of HPM presented in this study hinges on the concept of representing the solution as an infinite series sum. This approach exhibits rapid convergence to the precise solution, enabled by the use of a control parameter. The parameter region is initially determined, followed by the selection of a single value that ensures convergence with a satisfactory sum count.
- Subjects
PROBLEM solving; PLASMA waves; INFINITE series (Mathematics); ELECTRIC power transmission; FLUID flow; TRANSMISSION of sound; EULER-Bernoulli beam theory; ELASTIC wave propagation
- Publication
Mathematical Modelling of Engineering Problems, 2024, Vol 11, Issue 1, p273
- ISSN
2369-0739
- Publication type
Article
- DOI
10.18280/mmep.110130