Abstract
This paper examines the numerical solution of the nonlinear Fisher equation that is used to find the growth of tumour cells in the brain. By employing new methods that transform nonlinear partial differential equations (PDE) into nonlinear ordinary differential equations (ODE) through spatial discretization. The stability of the resulting nonlinear system is evaluated using Lyapunov’s criteria. Implicit stiff solvers, including various orders of backward differentiation formulas, are used to address the ODE system. The efficiency of these numerical methods is demonstrated through two examples, and a comparison with existing methods from the literature is conducted. Compared to traditional methods, the proposed numerical techniques are distinguished by their simplicity, precision, and remarkable efficiency.
Recommended Citation
Vimal, Vikash; Sinha, Rajesh Kumar; and Pannikkal, Liju
(2024).
(SI13-09) Numerical Methods for Solving Nonlinear Fisher Equation using Backward Differentiation Formula,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 19,
Iss.
4, Article 4.
Available at:
https://digitalcommons.pvamu.edu/aam/vol19/iss4/4