1. Apply the Fourier analysis to determine the critical time step for a 1-D transient heat conduction with the Runge–Kutta scheme of second order for time integration and with linear elements for...

1. Apply the Fourier analysis to determine the critical time step for a 1-D transient heat conduction with the Runge–Kutta scheme of second order for time integration and with linear elements for spatial discretization.

2. Starting from Equation 5.6 and assuming A is a function of T, derive Equation 5.14.

Consider the first order hyperbolic equation,

Calculate the characteristic curves and plot the characteristic curves emanating from x = 0.5 and x = 1.5. Calculate the time at which the two curves meet.