Solving the nonlinear forced Fisher equation PDE using a proposed generalized tanh-like ansatz method

Authors

  • Beatrice V. Bayan Department of Physics and Ateneo Research Institute of Science and Engineering, Ateneo de Manila University
  • Benjamin B. Dingel Department of Physics and Ateneo Research Institute of Science and Engineering, Ateneo de Manila University, and Nasfine Photonics Inc.

Abstract

The standard or homogeneous Fisher equation (FE) is a deterministic approximation to a stochastic model, commonly used to represent the spatial spread of gene selection and migration. It is a natural extension of the logistic growth population. This partial differential equation (PDE) can be solved using the tanh method. However, when an inhomogeneous driving function is introduced to FE, the tanh method fails. This paper proposes a new tanh-like function, the Generalized Half-Angle Tangent Hyperbolic (we called g-HATH), given as Yp(ξ)=(1+p)[tanh⁡(ξ/2)/(1 + p⁡ tanh2(ξ/2)] as a new ansatz with variable p (0 ≤ p ≤ 1). It reduces to the tanh(ξ) when p = 1, and tanh(ξ/2) when p = 0. The new ansatz introduces a new approach to solving a broader class of nonlinear partial differential equations, allowing solutions to more complex phenomena involving inhomogeneous PDEs in natural science, social science, or physical science.

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Issue

Article ID

SPP-2024-PC-10

Section

Poster Session C (Theoretical and Mathematical Physics)

Published

2024-06-25

How to Cite

[1]
BV Bayan and BB Dingel, Solving the nonlinear forced Fisher equation PDE using a proposed generalized tanh-like ansatz method, Proceedings of the Samahang Pisika ng Pilipinas 42, SPP-2024-PC-10 (2024). URL: https://proceedings.spp-online.org/article/view/SPP-2024-PC-10.