Wyniki wyszukiwania - BazTech

1

Finite difference method for the fractional order pseudo telegraph integro-differential equation

Modanli Mahmut, Ozbag Fatih, Akgül Ali

Journal of Applied Mathematics and Computational Mechanics

|

2022

|

Vol. 21, nr 1

41--54

EN

The main goal of this paper is to investigate the numerical solution of the fractional order pseudo telegraph integro-differential equation. We establish the first order finite difference scheme. Then for the stability analysis of the constructed difference scheme, we give theoretical statements and prove them. We also support our theoretical statements by performing numerical experiments for some fractions of order α.

2

An optimal 125-point scheme for 3D frequency-domain scalar wave equation

Yang Lingyun, Wu Guochen, Wang Yunliang, Li Qingyang, Zhang Hao

Acta Geophysica

|

2022

|

Vol. 70, no 1

71--88

EN

To improve accuracy and efficiency of forward modeling in the frequency domain, a 125-point finite-difference scheme is proposed. At present, the optimized difference format based on the rotating coordinate system is widely used, but it only suitable for equally sampling interval, and the optimized difference format based on the average-derivative method can be applied to different spaced sampling while improving the sampling accuracy. In this paper, we firstly introduce a 125-point optimized scheme for the three dimensional scalar wave equation. Then, according to the optimized difference scheme, the 125-point optimized difference coefficient is calculated for different spatial sampling spacing ratios. Compared with the optimal 27-point scheme, grid points number reduces from 4 points to 2.5 per wavelength, higher efficiency and suitable for unequal directional sampling intervals. In addition, the higher accuracy of 125-point scheme means it requires more storage and computation cost. Numerical results show that the optimized 125-point difference format has higher accuracy than the classical 27-point difference format.

3

Third order singularly perturbed delay differential equation of reaction diffusion type with integral boundary condition

Sekar Elango, Tamilselvan Ayyadurai

Journal of Applied Mathematics and Computational Mechanics

|

2019

|

Vol. 18, nr 2

99--110

EN

A class of third order singularly perturbed delay differential equations of reaction diffusion type with an integral boundary condition is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The method suggested is of almost first order convergent. An error estimate is derived in the discrete norm. Numerical examples are presented, which validate the theoretical estimates.

4

Probabilistic solutions of a stretched beam discretized with finite difference scheme and excited by Kanai–Tajimiground motion

Er G.-K., Iu V. P., Du H.-E.

Archives of Mechanics

|

2019

|

Vol. 71, nr 4-5

433--457

EN

The probabilistic solutions of the elastic stretched beam are studied under the excitation of Kanai–Tajimi ground motion. Finite difference scheme is adopted to formulate the nonlinear multi-degree-of-freedom system about the random vibration of the beam. The state-space-split is employed to make the high-dimensional Fokker–Planck–Kolmogorov equation reduced to 4-dimensional Fokker–Planck–Kolmogorov equations which are solved by the exponential polynomial closure method for the probabilistic solutions of the system responses. The rules for selecting the state variables are proposed in order to reduce the dimensionality of Fokker–Planck–Kolmogorov equation by the state-space-split method. The numerical results obtained by the state-space-split and exponential polynomial closure method, Monte Carlo simulation method, and equivalent linearization method are presented and compared to show the computational efficiency and numerical accuracy of the state-space-split and exponential polynomial closure method in analyzing the probabilistic solutions of thestrongly nonlinear stretched beam systems formulated by a finite difference scheme and excited by the Kanai–Tajimi ground motion.

5

Numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument

Abregov M. H., Kanchukoev V. Z., Shardanova M. A.

Journal of Applied Analysis

|

2017

|

Vol. 23, nr 2

141--146

EN

This work is devoted to the numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument in minor terms. The sufficient conditions of the one-valued solvability are established, and the a priori estimate of the solution is obtained. For the numerical solution, the problem studied is reduced to the equivalent boundary value problem for an ordinary linear differential equation of fourth order, for which the finite-difference scheme of second-order approximation was built. The convergence of this scheme to the exact solution is shown under certain conditions of the solvability of the initial problem. To solve the finite-difference problem, the method of five-point marching of schemes is used.

6

Implicit solution of 1d nonlinear porous medium equation using the four-point Newton- EGMSOR iterative method

Chew J. V. L., Sulaiman J.

Journal of Applied Mathematics and Computational Mechanics

|

2016

|

Vol. 15, nr 2

11--21

EN

The numerical method can be a good choice in solving nonlinear partial differential equations (PDEs) due to the difficulty in finding the analytical solution. Porous medium equation (PME) is one of the nonlinear PDEs which exists in many realistic problems. This paper proposes a four-point Newton-EGMSOR (4-Newton-EGMSOR) iterative method in solving 1D nonlinear PMEs. The reliability of the 4-Newton-EGMSOR iterative method in computing approximate solutions for several selected PME problems is shown with comparison to 4-Newton-EGSOR, 4-Newton-EG and Newton-Gauss-Seidel methods. Numerical results showed that the proposed method is superior in terms of the number of iterations and computational time compared to the other three tested iterative methods.

7

Explicit Finite-Difference Scheme for the Numerical Solution of the Model Equation of Nonlinear Hereditary Oscillator with Variable-Order Fractional Derivatives

Parovik R. I.

Archives of Control Sciences

|

2016

|

Vol. 26, no. 3

429--435

EN

The paper deals with the model of variable-order nonlinear hereditary oscillator based on a numerical finite-difference scheme. Numerical experiments have been carried out to evaluate the stability and convergence of the difference scheme. It is argued that the approximation, stability and convergence are of the first order, while the scheme is stable and converges to the exact solution

8

A finite difference method for nonlinear parabolic-elliptic systems of second-order partial differential equations

Malec M., Sapa L.

Opuscula Mathematica

|

2007

|

Vol. 27, no. 2

259-289

EN

This paper deals with a finite difference method for a wide class of weakly coupled nonlinear second-order partial differential systems with initial condition and weakly coupled nonlinear implicit boundary conditions. One part of each system is of the parabolic type (degenerated parabolic equations) and the other of the elliptic type (equations with a parameter) in a cube in R1+n. A suitable finite difference scheme is constructed. It is proved that the scheme has a unique solution, and the numerical method is consistent, convergent and stable. The error estimate is given. Moreover, by the method, the differential problem has at most one classical solution. The proof is based on the Banach fixed-point theorem, the maximum principle for difference functional systems of the parabolic type and some new difference inequalities. It is a new technique of studying the mixed-type systems. Examples of physical applications and numerical experiments are presented.

9

Flow characteristics in a vascular tube with an overIapping constriction

Pramanik S., Mukhopadhyay S., Layek G. C., Samad S. A.

International Journal of Applied Mechanics and Engineering

|

2007

|

Vol. 12, no 1

153-167

EN

A numerical solution to the unsteady blood flow in the neighbourhood of an overlapping constriction is obtained under laminar flow conditions. Blood is modelled as a viscous, incompressible and of Newtonian type fluid. A finite-difference staggered grid has been used to solve the unsteady incompressible Navier-Stokes equations in cylindrical polar co-ordinates under the axi-symmetric conditions. A co-ordinate transformation has been employed to map the constricted tube into a straight tube. The effect of flow characteristics in this type of constriction and its consequences in arterial diseases are investigated. Flow features such as velocity, pressure and wall shear stress distributions are presented graphically. The secondary separation has been noted in the downstream of the overlapping constriction when the Reynolds number of the flow is about 205.

10

A new grid block system for reducing grid orientation effect in oil reservoir simulation processes

Chong E., Syihab Z., Putra E., Hidayati D. T., Schechter D. S.

Archives of Mining Sciences

|

2006

|

Vol. 51, no 3

371-390

EN

The grid orientation effect (OOE) is a long-standing problem plaguing reservoir simulators that employ finite difference schemes. A rotation of the computational grids yields a substantially different solution under certain circumstances. A Cartesian grid witb one axis parallel to the line joining an injector and producer gives a solution significantly different from a grid that has the axes oriented at 45° to this line. This paper presents a new grid system that can reduce the grid orientation effect. This system involves using a unique grid-block assignment where rectangular grid blocks are interspersed with octagonal grid blocks. The boundaries are populated with triangular grid blocks. The entire domain consists of a "structured" grid block system referred to as the Hybrid Grid Block (HGB).

PL

W pracy rozważany jest efekt orientacji siatki numerycznej w procesie symulacji złoża węglowodorowego z wykorzystaniem różnic skończonych. Obrót siatki obliczeniowej daje w pewnych okolicznościach znacząco różne wyniki. Siatka prostokątna z jedną osią równoległą do linii łączącej odwiert eksploatacyjny i odwiert iniekcyjny daje rozwiązanie różne od siatki, w której osie są obrócone o kąt 45° w stosunku do wymienionej linii. Niniejszy artykuł pokazuje nowy system siatkowy, który może zredukować ten efekt orientacji siatki numerycznej. Autorzy proponują nowy system, zakładający użycie jednoznacznie opisanego bloku siatki, w którym bloki siatki prostokątnej są wymieszane z blokami siatki ortogonalnej. Obszary brzegowe są wypełnione siatką trójkątną. Zasadniczy obszar modelowania składa się z systemu siatki "strukturalnej" oznaczonej jako blok siatki hybrydowej (Hybrid grid Block - HGB). Artykuł zawiera szereg ciekawych eksperymentów numerycznych, ilustowany jest bogato wynikami modelowania.

11

Ocena przydatności różnicowej metody numerycznej do wyznaczania rozkładu temperatur w żebrze

Laskowski S.

Folia Societatis Scientiarum Lublinensis

|

2003

|

vol. 12

7-17

PL

W pracy przedstawiono wykorzystanie różnicowej metody numerycznej do wyznaczania rozkładu temperatur w żebrze. Dokładność zaprezentowanej metody oszacowano porównując uzyskane wyniki obliczeń z analitycznym rozwiązaniem dyskutowanego zagadnienia.

EN

A numerical method for obtaining temperature distribution in a fin is discussed in this paper. The accuracy of the method is evaluated by comparison with the analytical solution.