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Cited by 21 publications
(25 citation statements)
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“…[4,7,15,19] order of the scheme, we choose the numerical solution with sufficiently small grid spacing h and time-step size τ as the reference solution. In Table 3 Example 3 Finally, we consider the following problem:…”
Section: Numerical Experimentsmentioning
confidence: 99%
See 1 more Smart Citation
“…[4,7,15,19] order of the scheme, we choose the numerical solution with sufficiently small grid spacing h and time-step size τ as the reference solution. In Table 3 Example 3 Finally, we consider the following problem:…”
Section: Numerical Experimentsmentioning
confidence: 99%
“…As for the classical cases, many conservative and nonconservative numerical schemes have been constructed (see, e.g. [4,7,15,19]). But almost all of these numerical methods are nonlinear and conditionally stable, which is unfavourable on implementation.…”
Section: Introductionmentioning
confidence: 99%
“…These discretization schemes have been shown by analytical and numerical results to have better numerical and higher accuracy approximations than the standard second‐order finite difference schemes . References introduce research works have been conducted in recent years in the field of high‐order finite difference methods for solving different models.…”
Section: Introductionmentioning
confidence: 99%
“…These discretization schemes have been shown by analytical and numerical results to have better numerical and higher accuracy approximations than the standard second-order finite difference schemes [22][23][24][25][26]. References [27][28][29][30][31] introduce research works have been conducted in recent years in the field of high-order finite difference methods for solving different models. Another significant subject in numerical computation of partial differential equations is to efficiently solve the sparse linear systems arising from the discretized partial differential equations.…”
Section: Introductionmentioning
confidence: 99%
“…In order to improve accuracy in spatial direction, Guo et al [27] and Cao et al [28] introduced the energy conserving LDG methods and obtained optimal convergence or superconvergence of the method. Li et al [29,30] introduced the compact finite difference methods and investigated fully discrete numerical schemes for cubic NLSE with wave operator (i.e., f (s) = s). As far as we know, there are few results on construction of conservative compact finite difference methods for the generalized NLSE with wave operator (1.1).…”
Section: Introductionmentioning
confidence: 99%