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On the Bivariate Spectral Homotopy Analysis Method Approach for Solving Nonlinear Evolution Partial Differential Equations

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  • S. S. Motsa

Abstract

This paper presents a new application of the homotopy analysis method (HAM) for solving evolution equations described in terms of nonlinear partial differential equations (PDEs). The new approach, termed bivariate spectral homotopy analysis method (BISHAM), is based on the use of bivariate Lagrange interpolation in the so-called rule of solution expression of the HAM algorithm. The applicability of the new approach has been demonstrated by application on several examples of nonlinear evolution PDEs, namely, Fisher’s, Burgers-Fisher’s, Burger-Huxley’s, and Fitzhugh-Nagumo’s equations. Comparison with known exact results from literature has been used to confirm accuracy and effectiveness of the proposed method.

Suggested Citation

  • S. S. Motsa, 2014. "On the Bivariate Spectral Homotopy Analysis Method Approach for Solving Nonlinear Evolution Partial Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, August.
    • Handle: RePEc:hin:jnlaaa:350529
    DOI: 10.1155/2014/350529
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    Cited by:

    1. Elias Mwakilama & Vusi Magagula & Duncan Gathungu, 2023. "A Novel Multivariate Spectral Local Quasilinearization Method (MV‐SLQLM) for Modelling Flow, Moisture, Heat, and Solute Transport in Soil," Journal of Applied Mathematics, John Wiley & Sons, vol. 2023(1).
    2. T. M. Agbaje & P. G. L. Leach, 2020. "Numerical Investigation of Natural Convection Viscoelastic Jeffrey’s Nanofluid Flow from a Vertical Permeable Flat Plate with Heat Generation, Thermal Radiation, and Chemical Reaction," Abstract and Applied Analysis, John Wiley & Sons, vol. 2020(1).
    3. Titilayo Morenike Agbaje & Gilbert Makanda, 2021. "Numerical Solutions for Laminar Boundary Layer Nanofluid Flow along with a Moving Cylinder with Heat Generation, Thermal Radiation, and Slip Parameter," Abstract and Applied Analysis, John Wiley & Sons, vol. 2021(1).

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