Three second-order accurate explicit finite-difference schemes—MacCormack’s method, Lambda scheme and Gabutti scheme—are introduced to solve the quasilinear, hyperbolic partial differential equations describing waterhammer phenomenon in closed conduits. The details of these schemes and the treatment of boundary conditions are presented. The results computed by using these schemes for a simple frictionless piping system are compared with the exact solution. It is shown that for the same accuracy, second-order schemes require fewer computational nodes and less computer time as compared to those required by the first-order characteristic method.