Final answer:
To solve the viscous Burgers equation using different schemes, you can use the FTCS explicit, MacCormack explicit, or BTCS implicit schemes.
Step-by-step explanation:
To solve the viscous Burgers equation using different schemes, we can use the following steps:
(a) FTCS explicit scheme: This scheme involves using a forward time central space (FTCS) method to discretize the equation in both time and space. It calculates the values at the next time step using the values at the current time step. The explicit scheme involves solving the equation explicitly for the values at the next time step.
(b) MacCormack explicit scheme: This scheme is an improvement on the FTCS scheme and involves two steps. In the first step, it calculates a predictor value for the next time step. In the second step, it corrects this predictor value using a corrector step. The explicit scheme involves solving both steps explicitly.
(c) BTCS implicit scheme: This scheme involves using a backward time central space (BTCS) method to discretize the equation in both time and space. It calculates the values at the next time step using the values at the current and next time steps. The implicit scheme involves solving the equation implicitly for the values at the next time step.