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Equivalent Power-Form Transformation For Fractal Bratu’S Equation

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  • ALEX ELà AS-ZÚÑIGA

    (Department of Mechanical Engineering and Advanced Materials, School of Engineering and Science, Tecnologico de Monterrey, Av. E. Garza Sada 2501 Sur, Monterrey, Nuevo León, 64849, México)

  • LUIS MANUEL PALACIOS-PINEDA

    (��Tecnológico Nacional de México, Instituto Tecnológico de Pachuca, Carretera México - Pachuca Km. 87.5, C.P. 42080, Colonia Venta Prieta, Pachuca de Soto, Hgo., Mexico)

  • ISAAC H. JIMÉNEZ-CEDEÑO

    (��Engineering Department, Safran Mexico Av. Ishikawa # 1001, (Esquina con Av. Taguchi) Parque Industrial Supra, C.P. 31183, Chihuahua, Ch., Mexico)

  • OSCAR MARTÃ NEZ-ROMERO

    (Department of Mechanical Engineering and Advanced Materials, School of Engineering and Science, Tecnologico de Monterrey, Av. E. Garza Sada 2501 Sur, Monterrey, Nuevo León, 64849, México)

  • DANIEL OLVERA TREJO

    (Department of Mechanical Engineering and Advanced Materials, School of Engineering and Science, Tecnologico de Monterrey, Av. E. Garza Sada 2501 Sur, Monterrey, Nuevo León, 64849, México)

Abstract

In this paper, an equivalent power-form transformation method with a weighted function is applied for solving the one-dimensional fractal Bratu’s boundary value equation. Numerical integration solutions obtained from the equivalent Bratu’s equation as well as those from its approximate Taylor’s series solution reveal that the proposed methodology yields highly accurate solutions. Therefore, it is believed that by applying the power-form transformation, various fractal differential equations in which two scales are needed because of the physical laws involved in modeling the observed phenomena, can be solved by treating the nonlinear terms as equivalent power-form terms.

Suggested Citation

  • Alex Elã As-Zãšã‘Iga & Luis Manuel Palacios-Pineda & Isaac H. Jimã‰Nez-Cedeã‘O & Oscar Martã Nez-Romero & Daniel Olvera Trejo, 2021. "Equivalent Power-Form Transformation For Fractal Bratu’S Equation," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(01), pages 1-8, February.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:01:n:s0218348x21500195
    DOI: 10.1142/S0218348X21500195
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