Question

Consider the following initial and boundary value problem ∂u/∂t - ∂²u/∂²t = 1,00 u(0,t) =1, ∂u/∂x (1,t) = 0,t>1 a) Use the Matlab code FW_Euler_heat.m to solve (p.82) to solve for a numerical solution of the problem b) Use separation of variables to find the Fourier series solution of the problem.

Answer 1

To solve the initial and boundary value problem, use the Matlab code FW_Euler_heat.m for a numerical solution. To find the Fourier series solution, use separation of variables and apply boundary conditions.

Step-by-step explanation:

To solve the given initial and boundary value problem using the Matlab code FW_Euler_heat.m, follow the steps below:

1. Download the Matlab code FW_Euler_heat.m.
2. Open the Matlab software and run the code.
3. The code will generate a numerical solution for the problem.

To find the Fourier series solution of the problem using separation of variables, follow these steps:

1. Assume the solution can be represented as a sum of Fourier series.
2. Apply the boundary conditions to determine the coefficients of the Fourier series.