The stability of difference schemes of a higher dimensional parabolic equation

1991 ◽  
Vol 12 (12) ◽  
pp. 1209-1215
Author(s):  
Sun Qi-ren
Keyword(s):  
Parabolic Equation ◽  
Difference Schemes ◽  
Stability Of Difference Schemes ◽  
Higher Dimensional ◽  
The Stability

scholarly journals Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Abdon Atangana ◽  
Dumitru Baleanu
Keyword(s):  
Parabolic Equation ◽  
Fractional Calculus ◽  
Numerical Solution ◽  
Parabolic Equations ◽  
Difference Schemes ◽  
Stability And Convergence ◽  
Implicit Schemes ◽  
The Stability

A kind of parabolic equation was extended to the concept of fractional calculus. The resulting equation is, however, difficult to handle analytically. Therefore, we presented the numerical solution via the explicit and the implicit schemes. We presented together the stability and convergence of this time-fractional parabolic equation with two difference schemes. The explicit and the implicit schemes in this case are stable under some conditions.

scholarly journals Stability of delay parabolic difference equations

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 995-1006 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Deniz Agirseven
Keyword(s):  
Parabolic Equations ◽  
Approximate Solutions ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Unbounded Operators ◽  
Stability Of Difference Schemes ◽  
Fractional Spaces ◽  
The Stability ◽  
Delay Differential ◽  
Parabolic Difference

In the present paper, the stability of difference schemes for the approximate solution of the initial value problem for delay differential equations with unbounded operators acting on delay terms in an arbitrary Banach space is studied. Theorems on stability of these difference schemes in fractional spaces are established. In practice, the stability estimates in H?lder norms for the solutions of difference schemes for the approximate solutions of the mixed problems for delay parabolic equations are obtained.

scholarly journals Economical factorized schemes for third-order pseudoparabolic equations

2021 ◽  
pp. 44-57
Author(s):  
Мурат Хамидбиевич Бештоков
Keyword(s):  
General Theory ◽  
Parabolic Equations ◽  
Difference Schemes ◽  
Stability And Convergence ◽  
Third Order ◽  
The Third ◽  
Stability Of Difference Schemes ◽  
The Stability ◽  
Pseudoparabolic Equations

Изучены экономичные факторизованные схемы для псевдопараболических уравнений третьего порядка. На основе общей теории устойчивости разностных схем доказаны устойчивость и сходимость разностных схем. Economical factorized schemes for pseudo-parabolic equations of the third order are studied. On the basis of the general theory of stability of difference schemes, the stability and convergence of difference schemes are proved.

The Maximum Principle and Some of Its Applications

2002 ◽  
Vol 2 (1) ◽  
pp. 50-91 ◽  
Author(s):  
Piotr Matus
Keyword(s):  
Maximum Principle ◽  
Order Approximation ◽  
Difference Schemes ◽  
Stability And Convergence ◽  
Finite Difference Schemes ◽  
The Maximum Principle ◽  
Stability Of Difference Schemes ◽  
Mixed Derivatives ◽  
The Subject ◽  
The Stability

AbstractThe subject of this paper is the maximum principle and its application for investigating the stability and convergence of finite difference schemes. To some extent, this is a survey of the works on constructing and investigating certain new classes of monotone difference schemes. In this connection the maximum principle for the derivatives discussed in this paper is of fundamental importance. It is used as a basis for proving the coefficient stability of difference schemes in Banach spaces and the monotonicity of economical schemes of full approximation. New results on unconditional stability of monotone difference schemes with weights, conservative explicit-implicit schemes (staggered schemes), monotone schemes of second-order approximation in arbitrary domains, and monotone difference schemes for multidimensional elliptic equations with mixed derivatives are given.

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