Question

Use the MATLAB PDE solver to solve numerically the Fisher equation

student submitted image, transcription available below
subject to the boundary conditions
∂u/∂x(-8,t)=0,u(8,t)=0.7
and the initial condition
U(x,0) = { 0.2,IxI ≤ 1.1
0.7.IxI 1.1

Answer 1

In MATLAB, define the Fisher equation, initial conditions, and boundary conditions, and use the numerical PDE solver like pdepe to compute the solution.

Step-by-step explanation:

To solve the Fisher equation numerically in MATLAB using the PDE solver, first define the appropriate functions that represent the equation, initial conditions, and boundary conditions. In this case, you would create functions for the partial differential equation, which is the Fisher equation itself, initial conditions that set the values of u(x, 0) to 0.2 for |x| ≤ 1 and to 0.7 for |x| > 1, and boundary conditions, which dictate that ∂u/∂x(-8, t) = 0 and u(8, t) = 0.7. You then would use MATLAB's numerical solver, such as pdepe, to compute the solution to the Fisher equation over a specified spatial domain and time frame.