NUMERICAL-SOLUTION OF THE 1-DIMENSIONAL FISHERS EQUATION BY FINITE-ELEMENTS AND THE GALERKIN METHOD(2)

In Fisher's equation, the mechanism of logistic growth and linear diff usion are combined in order to model the spreading and proliferation o f 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 num erical solutions approximate those of the Fisher equation. By using a. particular type of form functions, the off-diagonal elements of the m atrix on the left-hand side of the ODE system become negligibly small, which makes a multiplication with the inverse of this matrix unnecess ary, and therefore, leads to a simpler and faster computer program wit h less memory and storage requirements. It can, therefore, be consider ed a borderline method between finite elements and finite differences. A simple growth model for coral reefs demonstrates the program's adap tability to practical applications.