On partially inexact HSS iteration methods for the complex symmetric linear systems in space fractional CNLS equations

Ran, Yu-Hong; Wang, Jungang; Wang, Dong-Ling

doi:10.1016/j.cam.2016.11.030

Cited by 5 publications

(4 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…9 for the space variables and the Caputo time-fractional derivative, respectively. Ran et al 10 presented a new preconditioner based on Hermitian and skew-Hermitian splitting (HSS) for Toeplitz-like matrix and proved that Krylov subspace methods with the proposed preconditioners converge very fast. Lei et al 11 used an implicit finite difference scheme to solve high-dimensional two-sided space fractional diffusion equations with variable diffusion coefficients, that is proven to be uniquely solvable, unconditionally stable and first-order convergent in the infinity norm.…”

Section: Andmentioning

confidence: 99%

See 1 more Smart Citation

A numerical framework for the approximate solution of fractional tumor-obesity model

Arshad

Băleanu

Defterli

et al. 2019

Int. J. Model. Simul. Sci. Comput.

View full text Add to dashboard Cite

In this paper, we have proposed the efficient numerical methods to solve a tumor-obesity model which involves two types of the fractional operators namely Caputo and Caputo-Fabrizio (CF). Stability and convergence of the proposed schemes using Caputo and CF fractional operators are analyzed. Numerical simulations are carried out to investigate the effect of low and high caloric diet on tumor dynamics of the generalized models. We perform the numerical simulations of the tumor-obesity model for different fractional order by varying immune response rate to compare the dynamics of the Caputo and CF fractional operators.

show abstract

Section: Andmentioning

confidence: 99%

“…Next, we solve fractional model (6) with Caputo and CF by using the numerical schemes (10) and (11). We focus on the immune response rate ρ.…”

Section: Numerical Simulationsmentioning

confidence: 99%

A numerical framework for the approximate solution of fractional tumor-obesity model

Arshad

Băleanu

Defterli

et al. 2019

Int. J. Model. Simul. Sci. Comput.

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

“…To deal with the matrix ıI + D − T , Ran et al proposed the partially inexact HSS (PIHSS [44]) iteration method, and the HSS-like iteration method [45]. Numerical results in [44] and [45] show that the PIHSS iteration method outperforms the HSS iteration method in terms of computing time, and the HSS-like iteration method has better behavior in terms of both iteration counts and computing time compared with the PIHSS iteration method. In [46], Ran et al came to a conclusion that the HSS-like preconditioner is more efficient than the HSS preconditioner and the AICD preconditioner when they are in conjunction with the Krylov subspace iteration methods.…”

Section: Introductionmentioning

confidence: 99%

Introduction to the Department of Cardiology in Nanjing First Hospital of Nanjing Medical University, China

Zhang

Chen

2020

European Heart Journal

View full text Add to dashboard Cite

Reclosure of ruptured incision after peroral endoscopic myotomy using endoloops and metallic clipsSince Inoue et al. introduced peroral endoscopic myotomy (POEM) into a clinic to treat esophageal achalasia in 2010, the procedure has been carried out in many countries around the world. 1 As more and more POEM is being done, associated technical difficulties and complications may occur. 2 To our knowledge, the present study is the first to report incision rupture after POEM.A 37-year-old man presented to our academic center after experiencing 25 years of dysphagia and 2 months of exacerbation. Barium swallow examination and esophageal manometry diagnosed the patient with type I esophageal achalasia and he agreed to receive POEM.POEM was carried out using the standard technique. After the operation, the patient received routine postoperative care. On the third day after the procedure, the patient had a fever (38.9°C, white blood cell count 18.24 × 10 9 /L, % neutrophils 95.3%) and X-ray showed the absence of several metal clips at the proximal end of the longitudinal incision which revealed the incision rupture.Gastroesophageal endoscopy showed that the middle and proximal parts of the incision was ruptured. It was not possible to reclose the incision with routine clips because of the swollen mucosa around the defect. On endoscopy, an endoloop was inserted and snared the remaining clips in the distal part. In the middle, four clips were anchored onto the defect margins at full thickness and another endoloop was inserted to snare the clips tightly. The same procedure was done in the proximal part (Figs 1,2). After monitoring the patient's condition for several days, he was discharged without any complaints or complications.In the present study, we propose reclosure of a mucosal incision after POEM using conventional endoloops and hemostatic clips. It could reclose the incision regardless of the swollen tissue or the size of the longitudinal incision.

show abstract

An efficient block Gauss–Seidel iteration method for the space fractional coupled nonlinear Schrödinger equations

Dai

2021

Applied Mathematics Letters

View full text Add to dashboard Cite

On partially inexact HSS iteration methods for the complex symmetric linear systems in space fractional CNLS equations

Cited by 5 publications

References 18 publications

A numerical framework for the approximate solution of fractional tumor-obesity model

A numerical framework for the approximate solution of fractional tumor-obesity model

Introduction to the Department of Cardiology in Nanjing First Hospital of Nanjing Medical University, China

An efficient block Gauss–Seidel iteration method for the space fractional coupled nonlinear Schrödinger equations

Contact Info

Product

Resources

About