scholarly journals A fitted operator method for a model arising in vascular tumor dynamics

2020 ◽  
Keyword(s):  
Operator Method ◽  
Vascular Tumor ◽  
Fitted Operator

scholarly journals Accelerated Exponentially Fitted Operator Method for Singularly Perturbed Problems with Integral Boundary Condition

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Habtamu Garoma Debela ◽  
Gemechis File Duressa
Keyword(s):  
Boundary Condition ◽  
Numerical Integration ◽  
Operator Method ◽  
Singularly Perturbed ◽  
Integral Boundary Condition ◽  
Singularly Perturbed Problems ◽  
Integral Boundary ◽  
Uniformly Convergent ◽  
Exponentially Fitted ◽  
Fitted Operator

In this paper, we consider a class of singularly perturbed differential equations of convection diffusion type with integral boundary condition. An accelerated uniformly convergent numerical method is constructed via exponentially fitted operator method using Richardson extrapolation techniques and numerical integration methods to solve the problem. The integral boundary condition is treated using numerical integration techniques. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent.

scholarly journals Exponential Fitted Operator Method for Singularly Perturbed Convection-Diffusion Type Problems with Nonlocal Boundary Condition

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Habtamu Garoma Debela
Keyword(s):  
Boundary Condition ◽  
Differential Equations ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Operator Method ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Diffusion Type ◽  
Convection Diffusion ◽  
Fitted Operator

This paper presents the study of singularly perturbed differential equations of convection-diffusion type with nonlocal boundary condition. The proposed numerical scheme is a combination of the classical finite difference method for the boundary conditions and exponential fitted operator method for the differential equations at the interior points. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical examples considered. The method is shown to be first-order accuracy independent of the perturbation parameter ε .

scholarly journals A Dynamical Study of Fusion Hindrance with Nakajima-Zwanzig Projection Method

2021 ◽  
Author(s):  
Yasuhisa Abe ◽  
David Boilley ◽  
Quentin Hourdillé ◽  
Caiwan Shen
Keyword(s):  
Cross Sections ◽  
Degrees Of Freedom ◽  
Operator Method ◽  
Initial Distribution ◽  
Physical Parameters ◽  
Relaxation Processes ◽  
Fast Variable ◽  
Dynamical Study ◽  
Injection Point ◽  
Slow Variables

Abstract A new framework is proposed for the study of collisions between very heavy ions which lead to the synthesis of Super-Heavy Elements (SHE), to address the fusion hindrance phenomenon. The dynamics of the reaction is studied in terms of collective degrees of freedom undergoing relaxation processes with different time scales. The Nakajima-Zwanzig projection operator method is employed to eliminate fast variable and derive a dynamical equation for the reduced system with only slow variables. There, the time evolution operator is renormalised and an inhomogeneous term appears, which represents a propagation of the given initial distribution. The term results in a slip to the initial values of the slow variables. We expect that gives a dynamical origin of the so-called “injection point s” introduced by Swiatecki et al in order to reproduce absolute values of measured cross sections for SHE. A formula for the slip is given in terms of physical parameters of the system, which confirms the results recently obtained with a Langevin equation, and permits us to compare various incident channels.

scholarly journals Intestinal intussusception and progressive anemia due to pyogenic granuloma of the ileum: a case report

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Kodai Nagakari ◽  
Akikazu Yago ◽  
Yu Ohkura ◽  
Daisuke Tomita ◽  
Shusuke Haruta ◽  
...  
Keyword(s):  
Small Bowel ◽  
English Literature ◽  
Laboratory Data ◽  
Pyogenic Granuloma ◽  
Vascular Tumor ◽  
Small Bowel Resection ◽  
Intestinal Intussusception ◽  
Enhanced Computed Tomography ◽  
Laparoscopic Assisted ◽  
Progressive Anemia

Abstract Background Pyogenic granuloma is a benign vascular tumor, usually occurring on the skin or in the oral cavity. Small intestinal pyogenic granuloma is extremely rare, but intestinal intussusception due to the tumor is even rarer. Only 3 cases have been reported in the English literature at this writing. Case presentation An 86-year-old woman presented with abdominal pain and vomiting. Laboratory data discovered anemia. Contrast-enhanced computed tomography revealed small bowel obstruction due to intestinal intussusception. After decompression by long tube for 1 week, the obstruction did not improve and the anemia got worse. Therefore, laparoscopic assisted small bowel resection was performed as a diagnostic therapy. Pathology confirmed the diagnosis of pyogenic granuloma. The postoperative course was uneventful and the patient was discharged 10 days after surgery. Conclusions We experienced a case of intestinal intussusception and progressive anemia due to pyogenic granuloma of the ileum. Although the condition is extremely rare, surgeons must take into consideration the tumor in similar cases, and complete surgical resection is required.

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