scholarly journals An Unconditionally Stable Parallel Difference Scheme for Telegraph Equation

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
A. Borhanifar ◽  
Reza Abazari
Keyword(s):  
Difference Scheme ◽  
Domain Decomposition ◽  
Numerical Experiments ◽  
Telegraph Equation ◽  
Unconditional Stability ◽  
Implicit Method ◽  
Alternating Group ◽  
Unconditionally Stable ◽  
Parallel Difference ◽  
Stability And Accuracy

We use an unconditionally stable parallel difference scheme to solve telegraph equation. This method is based on domain decomposition concept and using asymmetric Saul'yev schemes for internal nodes of each sub-domain and alternating group implicit method for sub-domain's interfacial nodes. This new method has several advantages such as: good parallelism, unconditional stability and better accuracy than original Saul'yev schemes. The details of implementation and proving stability are briefly discussed. Numerical experiments on stability and accuracy are also presented.

scholarly journals Weak solvability of the unconditionally stable difference scheme for the coupled sine-Gordon system

2020 ◽  
Vol 25 (6) ◽  
pp. 997-1014
Author(s):  
Ozgur Yildirim ◽  
Meltem Uzun
Keyword(s):  
Difference Scheme ◽  
Numerical Method ◽  
Existence And Uniqueness ◽  
Numerical Experiments ◽  
Finite Difference Schemes ◽  
Order Of Accuracy ◽  
Unconditionally Stable ◽  
First Order ◽  
The Difference ◽  
Weak Solvability

In this paper, we study the existence and uniqueness of weak solution for the system of finite difference schemes for coupled sine-Gordon equations. A novel first order of accuracy unconditionally stable difference scheme is considered. The variational method also known as the energy method is applied to prove unique weak solvability.We also present a new unified numerical method for the approximate solution of this problem by combining the difference scheme and the fixed point iteration. A test problem is considered, and results of numerical experiments are presented with error analysis to verify the accuracy of the proposed numerical method.

The Mass-Preserving S-DDM Scheme for Two-Dimensional Parabolic Equations

2016 ◽  
Vol 19 (2) ◽  
pp. 411-441 ◽  
Author(s):  
Zhongguo Zhou ◽  
Dong Liang
Keyword(s):  
Domain Decomposition ◽  
Parabolic Equations ◽  
Numerical Experiments ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Time Step ◽  
Unconditionally Stable ◽  
One Dimensional ◽  
Splitting Technique ◽  
Theoretical Results

AbstractIn the paper, we develop and analyze a new mass-preserving splitting domain decomposition method over multiple sub-domains for solving parabolic equations. The domain is divided into non-overlapping multi-bock sub-domains. On the interfaces of sub-domains, the interface fluxes are computed by the semi-implicit (explicit) flux scheme. The solutions and fluxes in the interiors of sub-domains are computed by the splitting one-dimensional implicit solution-flux coupled scheme. The important feature is that the proposed scheme is mass conservative over multiple non-overlapping sub-domains. Analyzing the mass-preserving S-DDM scheme is difficult over non-overlapping multi-block sub-domains due to the combination of the splitting technique and the domain decomposition at each time step. We prove theoretically that our scheme satisfies conservation of mass over multi-block non-overlapping sub-domains and it is unconditionally stable. We further prove the convergence and obtain the error estimate in L2-norm. Numerical experiments confirm theoretical results.

A New Parallel Difference Numerical Method for the Payment of Dividend Black-Scholes Equation

2013 ◽  
Vol 756-759 ◽  
pp. 2744-2749
Author(s):  
Xiao Zhong Yang ◽  
Fan Zhang
Keyword(s):  
Numerical Method ◽  
Numerical Experiments ◽  
Unconditional Stability ◽  
Explicit Methods ◽  
New Methods ◽  
Black Scholes ◽  
Parallel Difference

A new alternating segment explicit-implicit and alternating segment implicit-explicit methods for solving the payment of dividend Black-Scholes equation are presented. These new methods have several advantages such as: good parallelism, unconditional stability, convergence and better accuracy. Numerical experiments show that the methods improve the calculation speed greatly.

High Accuracy Method for Magnetohydrodynamics System in Elsässer Variables

2015 ◽  
Vol 15 (1) ◽  
pp. 97-110 ◽  
Author(s):  
Nicholas Wilson ◽  
Alexander Labovsky ◽  
Catalin Trenchea
Keyword(s):  
Test Problem ◽  
Correction Method ◽  
High Accuracy ◽  
Unconditional Stability ◽  
Step Method ◽  
Order Accuracy ◽  
Unconditionally Stable ◽  
The Third ◽  
Coupling Terms ◽  
Mhd System

AbstractA method has been developed recently by the third author, that allows for decoupling of the evolutionary full magnetohydrodynamics (MHD) system in the Elsässer variables. The method entails the implicit discretization of the subproblem terms and the explicit discretization of coupling terms, and was proven to be unconditionally stable. In this paper we build on that result by introducing a high-order accurate deferred correction method, which also decouples the MHD system. We perform the full numerical analysis of the method, proving the unconditional stability and second order accuracy of the two-step method. We also use a test problem to verify numerically the claimed convergence rate.

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