Numerical study of fisher's equation by Adomian's method
Mathematical and Computer Modelling: An International Journal
A pseudospectral method of solution of Fisher's equation
Journal of Computational and Applied Mathematics
A wildland fire model with data assimilation
Mathematics and Computers in Simulation
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In Fisher's equation, the mechanism of logistic growth and linear diffusion are combined in order to model the spreading and proliferation of population, e.g., in ecological contexts. A Galerkin Finite Element method in two space dimensions is presented, which discretises a 1 + 2 dimensional version of this partial differential equation, and thus, providing a system of ordinary differential equations (ODEs) whose numerical solutions approximate those of the Fisher equation. By using a particular type of form functions, the off-diagonal elements of the matrix on the left-hand side of the ODE system become negligibly small, which makes a multiplication with the inverse of this matrix unnecessary, and therefore, leads to a simpler and faster computer program with less memory and storage requirements. It can, therefore, be considered a borderline method between finite elements and finite differences. A simple growth model for coral reefs demonstrates the program's adaptability to practical applications.