Open AccessLie point symmetries for generalised Fisher's equations describing tumour dynamics
Author(s) -
Salvador Chulián,
Álvaro Martínez-Rubio,
M. L. Gandarias,
María Rosa
Publication year - 2021
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2021164
Subject(s) - ordinary differential equation , partial differential equation , stochastic partial differential equation , integrating factor , mathematics , differential equation , numerical partial differential equations , ode , homogeneous space , variety (cybernetics) , examples of differential equations , exponential integrator , differential algebraic equation , mathematical analysis , statistics , geometry
A huge variety of phenomena are governed by ordinary differential equations (ODEs) and partial differential equations (PDEs). However, there is no general method to solve them. Obtaining solutions for differential equations is one of the greatest problem for both applied mathematics and physics. Multiple integration methods have been developed to the day to solve particular types of differential equations, specially those focused on physical or biological phenomena. In this work, we review several applications of the Lie method to obtain solutions of reaction-diffusion equations describing cell dynamics and tumour invasion.