The Novel Integral Homotopy Expansive Method

Uriel Filobello-Nino, Hector Vazquez-Leal, Jesus Huerta-Chua, Jaime Ramirez-Angulo, Darwin Mayorga-Cruz and Rogelio Alejandro Callejas-Molina
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Uriel Filobello-Nino: Facultad de Instrumentación Electrónica, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, Xalapa 91000, Mexico
Hector Vazquez-Leal: Facultad de Instrumentación Electrónica, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, Xalapa 91000, Mexico
Jesus Huerta-Chua: Instituto Tecnológico Superior de Poza Rica, Tecnológico Nacional de México, Luis Donaldo Colosio Murrieta S/N, Arroyo del Maíz, Poza Rica 93230, Mexico
Jaime Ramirez-Angulo: Instituto Tecnológico Superior de Poza Rica, Tecnológico Nacional de México, Luis Donaldo Colosio Murrieta S/N, Arroyo del Maíz, Poza Rica 93230, Mexico
Darwin Mayorga-Cruz: Consejo Veracruzano de Investigación Científica y Desarrollo Tecnológico (COVEICYDET), Av Rafael Murillo Vidal No. 1735, Cuauhtémoc, Xalapa 91069, Mexico
Rogelio Alejandro Callejas-Molina: Instituto Tecnológico de Celaya, Tecnológico Nacional de México, Antonio García Cubas Pte. 600, Celaya 38010, Mexico

Mathematics, 2021, vol. 9, issue 11, 1-18

Abstract: This work proposes the Integral Homotopy Expansive Method (IHEM) in order to find both analytical approximate and exact solutions for linear and nonlinear differential equations. The proposal consists of providing a versatile method able to provide analytical expressions that adequately describe the scientific phenomena considered. In this analysis, it is observed that the proposed solutions are compact and easy to evaluate, which is ideal for practical applications. The method expresses a differential equation as an integral equation and expresses the integrand of the equation in terms of a homotopy. As a matter of fact, IHEM will take advantage of the homotopy flexibility in order to introduce adjusting parameters and convenient functions with the purpose of acquiring better results. In a sequence, another advantage of IHEM is the chance to distribute one or more of the initial conditions in the different iterations of the proposed method. This scheme is employed in order to introduce some additional adjusting parameters with the purpose of acquiring accurate analytical approximate solutions.

Keywords: Integral Homotopy Expansive Method; homotopy analysis method; exact solution; approximate solution; linear and nonlinear ordinary differential equations; adjusting parameters (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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