A new numerical method for singularly perturbed turning point problems with two boundary layers based on reproducing kernel method

Geng, Fazhan; Qian, S.P.

doi:10.1007/s10092-016-0196-x

Cited by 7 publications

(1 citation statement)

References 29 publications

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“…The results in Table 6 and Fig. 8 show that the ASCD and CFD lead to stable and accurate results for the internal layer problem (26). The reason for absenting the stability restriction of CFD in solving internal layer problems is that the internal layer occurs at a turning point x = x in at which p(x in ) = 0.…”

Section: Figurementioning

confidence: 99%

Absolutely stable difference scheme for a general class of singular perturbation problems

et al. 2020

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This paper presents an absolutely stable noniterative difference scheme for solving a general class of singular perturbation problems having left, right, internal, or twin boundary layers. The original two-point second-order singular perturbation problem is approximated by a first-order delay differential equation with a variable deviating argument. This delay differential equation is transformed into a three-term difference equation that can be solved using the Thomas algorithm. The uniqueness and stability analysis are discussed, showing that the method is absolutely stable. An optimal estimate for the deviating argument is obtained to take advantage of the second-order accuracy of the central finite difference method in addition to the absolute stability property. Several problems having left, right, interior, or twin boundary layers are considered to validate and illustrate the method. The numerical results confirm that the deviating argument can stabilize the unstable discretized differential equation and that the new approach is effective in solving the considered class of singular perturbation problems.

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Section: Figurementioning

confidence: 99%