New Exact Solutions of One Nonlinear Equation in Mathematical Biology and Their Properties
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Summary
A comparison of the analytic results and the corresponding numerical calculations shows the importance of the exact solutions obtained for the solution of the generalized Fisher equation for nonlinear boundary-value problems with zero Neumann conditions.
- Type
- article
- Published
- 2001-10-01
- Cited by
- 13
- References
- 18
- OpenAlex
- https://openalex.org/W1735993
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:117589490
Keywords
Mathematics, Fisher equation, Exact solutions in general relativity, Zero (linguistics), Boundary value problem
References
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- Nonlinear Partial Differential Equations in Engineering
- Spatial segregation of interacting species.
- Decay to Uniform States in Ecological Interactions
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- Diffusion and the Predator-Prey Interaction
- Explicit solutions of Fisher's equation for a special wave speed
- On invariant solutions of the equation of non-linear heat conduction with a source
- A constructive method for obtaining new exact solutions of nonlinear evolution equations
- Diffusion, Self-Diffusion and Cross-Diffusion
- Group-invariant solutions of differential equations
- Application of one constructive method for the construction of non-Lie solutions of nonlinear evolution equations
- New exact solutions for a free boundary system
- THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES
- Lectures on nonlinear-differential-equation models in biology
- The mathematical theory of diffusion and reaction in permeable catalysts
- Mathematical Biology
Cited by
- Cubic B-splines collocation method for solving nonlinear parabolic partial differential equations with Neumann boundary conditions
- Numerical solutions of one-dimensional non-linear parabolic equations using Sinc collocation method
- Diffusive Lotka-Volterra System: Lie Symmetries and Exact and Numerical Solutions
- New exact solutions of a nonlinear cross-diffusion system
- Parabolic Partial Differential Equations as Inverse Moments Problem
- Lie symmetries of the shigesada-Kawasaki-Teramoto system
- Parabolic Partial Differential Equations with Border Conditions of Dirichlet as Inverse Moments Problem
- An efficient B-spline difference method for solving system of nonlinear parabolic PDEs
- A class of numerical algorithms based on cubic trigonometric B-spline functions for numerical simulation of nonlinear parabolic problems
- Exact traveling waves for a generalized Fisher’s equation
- Orthogonal cubic splines for the numerical solution of nonlinear parabolic partial differential equations
- The Shigesada-Kawasaki-Teramoto model: Conditional symmetries, exact solutions and their properties
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