Objective: Solve the heat equation numerically using finite difference methods with dirichlet or neumann conditions using explicit methods. Solve the heat equation shown for u(t,x) using the explicit time stepping method. диди dt dx² Initial condition: u(x, t = 0) = sin(xx) Boundary conditions: u(x = 0,t) = 0 u(x = L,t) = 0 Assume the dimensions in x are from 0 to 1 with Ax = 0.2. Consider times from 0 to 0.5 with At = 0.01. a) Name your solution matrix "u", where each column is a node in the x-direction and each row is a time. Plot several times to make sure the system behaves as expected. The size of u should be 51x6. b) Calculate the error between your solution and the analytical solution, u(x,t) = ex²sin(xx). This should be a matrix. Then calculate the infinity norm of the error matrix named "En". If you want to pre-check your analytical solution matrix name it "ua".