Parallelizable approximate solvers for recursions arising in preconditioning

Shapira, Yair

doi:10.1016/s0024-3795(97)00339-x

Cited by 1 publication

(4 citation statements)

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“…is pointwise small, at least in the outer domain. The accuracy of the upwind scheme for subproblem ((1)) follows from Lemmas 2 and 6 in [14]; indeed, because the matrix A = cL…”

Section: The 2-d Casementioning

confidence: 99%

“…The conclusion is that the transformation x = x(φ) is just the Liouville transformation for the Sturm-Liouville problem (13)- (14). In particular, L is symmetric with respect to the measure (dφ/dx) 2 dx = (dφ/dx)dφ.…”

Section: Symmetry In the Convection-diffusion Equationmentioning

confidence: 99%

“…Let x ≡ x(φ) be the unique solution of (13), (14) with f ≡ 0, and assume that x(φ) is a monotone function. For example, if a is a nonzero constant, then…”

Section: Symmetry In the Convection-diffusion Equationmentioning

confidence: 99%

“…Using this transformation, we have that the solution of (13), (14) with f ≡ 0 in terms of the dependent variable x is the identity function u(x) = x. Therefore, the representation of L in terms of the dependent variable x is L = g(x)d 2 u/dx 2 , for some function g. Indeed,…”

Section: Symmetry In the Convection-diffusion Equationmentioning

confidence: 99%

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Adequacy of finite difference schemes for convection‐diffusion equations

Shapira

2002

Numerical Methods Partial

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Finite difference schemes for the numerical solution of singularly perturbed convection problems on uniform grids are studied in the limit case where the viscosity and the meshsize approach zero at the same time. The present error estimates are given in terms of order of magnitude in the above limit process and are useful in a priori choosing adequate schemes and meshsizes for boundary-layer problems and problems with closed characteristics.

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“…is pointwise small, at least in the outer domain. The accuracy of the upwind scheme for subproblem ((1)) follows from Lemmas 2 and 6 in [14]; indeed, because the matrix A = cL…”

Section: The 2-d Casementioning

confidence: 99%

Section: Symmetry In the Convection-diffusion Equationmentioning

confidence: 99%

“…Let x ≡ x(φ) be the unique solution of (13), (14) with f ≡ 0, and assume that x(φ) is a monotone function. For example, if a is a nonzero constant, then…”

Section: Symmetry In the Convection-diffusion Equationmentioning

confidence: 99%

Section: Symmetry In the Convection-diffusion Equationmentioning

confidence: 99%

See 2 more Smart Citations