2022
DOI: 10.1016/j.amc.2021.126734
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Fast L2-1σ Galerkin FEMs for generalized nonlinear coupled Schrödinger equations with Caputo derivatives

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Cited by 7 publications
(6 citation statements)
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“…Remark The convergence estimates for the proposed numerical schemes hold under some restrictions on the time step that makes these schemes conditionally stable and conditionally convergent. In order to get rid of these restrictions, a temporal‐spatial error splitting scheme has been adopted in [33]. We are exploring this new technique to prove unconditional convergence estimates for the proposed numerical schemes in this work.…”
Section: Numerical Resultsmentioning
confidence: 99%
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“…Remark The convergence estimates for the proposed numerical schemes hold under some restrictions on the time step that makes these schemes conditionally stable and conditionally convergent. In order to get rid of these restrictions, a temporal‐spatial error splitting scheme has been adopted in [33]. We are exploring this new technique to prove unconditional convergence estimates for the proposed numerical schemes in this work.…”
Section: Numerical Resultsmentioning
confidence: 99%
“…This motivates the researchers to develop numerical algorithms for solving fractional partial differential equations. In the literature, these numerical algorithms mainly consist of finite difference in time and different approximations in space, for example, finite difference methods [25][26][27][28], spectral methods [29,30], finite element methods [31][32][33][34][35], virtual element methods [36,37], discontinuous Gelerkin methods [38,39], and mixed finite element methods [40,41].…”
Section: Introductionmentioning
confidence: 99%
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“…Recently, the temporal-spatial error splitting argument was widely used for analyzing the time fractional problems. The earlier work can be found in [8,16,19], where the unconditional convergence results were obtained by assuming that the solutions are smooth. Taking the initial singularity into account, some researchers obtained the unconditionally convergent results of the L1 scheme [17,29] and the Alikhanov scheme [41] based on graded meshes, i.e.…”
Section: Introductionmentioning
confidence: 99%