A. I. Asnor¹, S. A. M. Yatim¹, Z. B. Ibrahim², N. Zainuddin³

CMC-Computers, Materials & Continua, Vol.67, No.1, pp. 1253-1267, 2021, DOI:10.32604/cmc.2021.014781

Abstract Many initial value problems are difficult to be solved using ordinary, explicit step-by-step methods because most of these problems are considered stiff. Certain implicit methods, however, are capable of solving stiff ordinary differential equations (ODEs) usually found in most applied problems. This study aims to develop a new numerical method, namely the high order variable step variable order block backward differentiation formula (VSVO-HOBBDF) for the main purpose of approximating the solutions of third order ODEs. The computational work of the VSVO-HOBBDF method was carried out using the strategy of varying the step size and order in a single code. The… More >

A. Grimaldi¹, G. Pascazio², M. Napolitano³

CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.1, pp. 45-56, 2006, DOI:10.3970/cmes.2006.014.045

Abstract This paper provides a numerical method for solving two- and three-dimensional unsteady incompressible flows. The vorticity-velocity formulation of the Navier--Stokes equations is considered, employing the vorticity transport equation and a second-order Poisson equation for the velocity. Second-order-accurate centred finite differences on a staggered grid are used for the space discretization. The vorticity equation is discretized in time using a fully implicit three-level scheme. At each physical time level, a dual-time stepping technique is used to solve the coupled system of non linear algebraic equations by various efficient relaxation schemes. Steady flows are computed by dropping the physical time derivative and… More >