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In this paper, we consider a contaminant transport model with Langmuir sorption under nonequilibrium conditions which is described by two coupled equations. Three numerical methods are used namely; Euler scheme forward in space, Euler scheme backward in space and nonstandard finite difference (NSFD) schemes. We compare the performance of the three methods by computing some errors: L1 error, dispersion and dissipation errors for both coarse and fine grids and short and long propagation times. We also perform a spectral analysis of the dispersive and dissipative properties of the three methods for the transport model. [ABSTRACT FROM AUTHOR]

An unconditionally positive definite scheme has been derived in [1] to approximate a linear advection-diffusion-reaction equation which models exponential travelling waves and the coefficients of advective, diffusive and reactive terms have been chosen as one. The scheme has been baptised as Unconditionally Positive Finite Difference (UPFD). In this work, we use the UPFD scheme to solve the advection-diffusion-reaction problem in [1] and we also extend our study to three other important regimes involved in this model. The temporal step size is varied while fixing the spatial step size. We compute some errors namely; L1 error, dispersion, dissipation errors. We also study the variation of the modulus of the exact amplification factor, modulus of amplification factor of the scheme and relative phase error, all vs the phase angle for the four different regimes. [ABSTRACT FROM AUTHOR]

In this paper, three numerical methods have been used to solve a 1-D Convection-Diffusion equation with specified initial and boundary conditions. The methods used are the third order upwind scheme [1], fourth order upwind scheme [1] and a Non-Standard Finite Difference (NSFD) scheme [4]. The problem we considered has steep boundary layers near x = 1 [3] and this is a challenging test case as many schemes are plagued by nonphysical oscillation near steep boundaries. We compute the L2 and L∞ errors, dissipation and dispersion errors when the three numerical schemes are used and observe that the NSFD is much better than the other two schemes for both coarse and fine grids and also at low and high Reynolds numbers. [ABSTRACT FROM AUTHOR]