scholarly journals Investigations for a Type of Variable Coefficient Fractional Subdiffusion Equation with Multidelay

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Wei Gu
Keyword(s):  
Difference Scheme ◽  
Variable Coefficient ◽  
Stability And Convergence ◽  
Numerical Tests ◽  
Convergence Results ◽  
Subdiffusion Equation ◽  
Theoretical Results

A difference scheme is constructed for a type of variable coefficient time fractional subdiffusion equation with multidelay. Stability and convergence results of the scheme are obtained, and theoretical results are proved by two numerical tests.

scholarly journals A Newton Linearized Crank-Nicolson Method for the Nonlinear Space Fractional Sobolev Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yifan Qin ◽  
Xiaocheng Yang ◽  
Yunzhu Ren ◽  
Yinghong Xu ◽  
Wahidullah Niazi
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Scheme ◽  
Difference Method ◽  
Stability And Convergence ◽  
Sobolev Equation ◽  
Numerical Examples ◽  
Convergence Orders ◽  
Theoretical Results ◽  
Crank Nicolson

In this paper, one class of finite difference scheme is proposed to solve nonlinear space fractional Sobolev equation based on the Crank-Nicolson (CN) method. Firstly, a fractional centered finite difference method in space and the CN method in time are utilized to discretize the original equation. Next, the existence, uniqueness, stability, and convergence of the numerical method are analyzed at length, and the convergence orders are proved to be O τ 2 + h 2 in the sense of l 2 -norm, H α / 2 -norm, and l ∞ -norm. Finally, the extensive numerical examples are carried out to verify our theoretical results and show the effectiveness of our algorithm in simulating spatial fractional Sobolev equation.

scholarly journals A Dufort-Frankel Difference Scheme for Two-Dimensional Sine-Gordon Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-22 ◽  
Author(s):  
Zongqi Liang ◽  
Yubin Yan ◽  
Guorong Cai
Keyword(s):  
Numerical Methods ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
The Stability ◽  
Predictor Corrector ◽  
Theoretical Results ◽  
Methods Numerical

A standard Crank-Nicolson finite-difference scheme and a Dufort-Frankel finite-difference scheme are introduced to solve two-dimensional damped and undamped sine-Gordon equations. The stability and convergence of the numerical methods are considered. To avoid solving the nonlinear system, the predictor-corrector techniques are applied in the numerical methods. Numerical examples are given to show that the numerical results are consistent with the theoretical results.

scholarly journals Factorized difference scheme for two-dimensional subdiffusion equation in nonhomogeneous media

2016 ◽  
Vol 99 (113) ◽  
pp. 1-13 ◽  
Author(s):  
Aleksandra Delic ◽  
Sandra Hodzic ◽  
Bosko Jovanovic
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Approximation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Nonhomogeneous Media ◽  
Subdiffusion Equation ◽  
Initial Boundary Value

A factorized finite-difference scheme for numerical approximation of initial-boundary value problem for two-dimensional subdiffusion equation in nonhomogeneous media is proposed. Its stability and convergence are investigated. The corresponding error bounds are obtained.

scholarly journals QUADRATIC SPLINE SUBDOMAIN METHOD FOR VOLTERRA INTEGRAL EQUATIONS

2005 ◽  
Vol 10 (4) ◽  
pp. 335-344 ◽  
Author(s):  
V. Deputat ◽  
P. Oja
Keyword(s):  
Boundary Condition ◽  
Uniform Boundedness ◽  
The Other ◽  
Stability And Convergence ◽  
Quadratic Spline ◽  
First Derivative ◽  
Numerical Tests ◽  
Quadratic Splines ◽  
Subdomain Method ◽  
Theoretical Results

In our work we consider the step‐by‐step and nonlocal subdomain methods with quadratic splines. We prove that the first method is unstable. In the case of nonlocal method we replaced the first derivative condition by a not‐a‐knot boundary condition at the other end of the interval of integration. As a result, we get stability of this method. Main results about stability and convergence are based on the uniform boundedness of quadratic spline histopolation projections. The numerical tests given at the end support the theoretical results.

H1 Stability and Convergence of the FE, FV and FD Methods for an Elliptic Equation

2013 ◽  
Vol 3 (2) ◽  
pp. 154-170 ◽  
Author(s):  
Yinnian He ◽  
Xinlong Feng
Keyword(s):  
Finite Element ◽  
Elliptic Equation ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Poisson Equation ◽  
Finite Volume ◽  
Stability And Convergence ◽  
Uniform Mesh ◽  
Numerical Tests ◽  
Theoretical Results

AbstractWe obtain the coefficient matrices of the finite element (FE), finite volume (FV) and finite difference (FD) methods based on P1-conforming elements on a quasi-uniform mesh, in order to approximately solve a boundary value problem involving the elliptic Poisson equation. The three methods are shown to possess the same H1-stability and convergence. Some numerical tests are made, to compare the numerical results from the three methods and to review our theoretical results.

scholarly journals A Compact Difference Scheme for a Class of Variable Coefficient Quasilinear Parabolic Equations with Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Wei Gu
Keyword(s):  
Difference Scheme ◽  
Variable Coefficient ◽  
Numerical Test ◽  
Parabolic Systems ◽  
Stability And Convergence ◽  
Compact Difference Scheme ◽  
Quasilinear Parabolic Equations ◽  
Compact Difference ◽  
The Difference ◽  
Equations With Delay

A linearized compact difference scheme is provided for a class of variable coefficient parabolic systems with delay. The unique solvability, unconditional stability, and convergence of the difference scheme are proved, where the convergence order is four in space and two in time. A numerical test is presented to illustrate the theoretical results.

scholarly journals A Crank-Nicolson Difference Scheme for Solving a Type of Variable Coefficient Delay Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Wei Gu ◽  
Peng Wang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Scheme ◽  
Variable Coefficient ◽  
Numerical Test ◽  
Partial Differential ◽  
The Difference ◽  
Delay Partial Differential Equations ◽  
Theoretical Results ◽  
Crank Nicolson

A linearized Crank-Nicolson difference scheme is constructed to solve a type of variable coefficient delay partial differential equations. The difference scheme is proved to be unconditionally stable and convergent, where the convergence order is two in both space and time. A numerical test is provided to illustrate the theoretical results.

scholarly journals Stable Filtering Procedures for Nodal Discontinuous Galerkin Methods

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Jan Nordström ◽  
Andrew R. Winters
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Finite Difference Methods ◽  
Basis Functions ◽  
Galerkin Methods ◽  
Theoretical Discussion ◽  
Numerical Tests ◽  
Dg Methods ◽  
Theoretical Results ◽  
Filtering Procedure

AbstractWe prove that the most common filtering procedure for nodal discontinuous Galerkin (DG) methods is stable. The proof exploits that the DG approximation is constructed from polynomial basis functions and that integrals are approximated with high-order accurate Legendre–Gauss–Lobatto quadrature. The theoretical discussion re-contextualizes stable filtering results for finite difference methods into the DG setting. Numerical tests verify and validate the underlying theoretical results.

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