The residual power series method for the one-dimensional unsteady flow of a van der Waals gas

A residual power series scheme is developed for mixed-type p-system of conservation laws. The residual power series method (RPSM) does not require discretization, reduces the system to an explicit system of algebraic equations and consequently of massive computations. Convergence hypotheses are discussed and error bounds of exponential rates are derived. The scheme is numerically tested to several cases of the van der Waals equations which arise in fluid dynamics. Stability is obtained graphically while transition through regions. The reported results reveal the reliability, efficiency and economical implementation of the proposed algorithm for handling nonlinear partial differential equations in applied mathematics. (C) 2018 Elsevier B.V. All rights reserved.