The lesson starts with writing of the parabolic equation, eigen value problem and modal decomposition of ‘d’ which have been already completed in previous lessons. The idea of modal decomposition is extended to the time exact ODEs and is substituted in these equations.
The use of modal decomposition for time-exact ODEs continues here. This derivation is done for an arbitrary eigen mode (vector) and holds for all values. The equation generated is the single degree of freedom modal equation. The same procedure is applied systematically to the time discrete homogeneous ODE and then the single degree of freedom modal equation is written for the time discrete problem.