scholarly journals An Approximation of Semigroups Method for Stochastic Parabolic Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Mehmet Emin San
Keyword(s):  
Difference Scheme ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Single Step ◽  
Nonlocal Boundary Value Problem ◽  
Convergence Estimate ◽  
Numerical Examples ◽  
Convergence Estimates ◽  
The Difference

A single-step difference scheme for the numerical solution of the nonlocal-boundary value problem for stochastic parabolic equations is presented. The convergence estimate for the solution of the difference scheme is established. In application, the convergence estimates for the solution of the difference scheme are obtained for two nonlocal-boundary value problems. The theoretical statements for the solution of this difference scheme are supported by numerical examples.

scholarly journals On Third Order Stable Difference Scheme for Hyperbolic Multipoint Nonlocal Boundary Value Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Ozgur Yildirim ◽  
Meltem Uzun
Keyword(s):  
Boundary Value Problem ◽  
Difference Scheme ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Stability Estimates ◽  
Nonlocal Boundary Value Problem ◽  
Third Order ◽  
Order Of Accuracy ◽  
Definite Operator ◽  
The Difference

This paper presents a third order of accuracy stable difference scheme for the approximate solution of multipoint nonlocal boundary value problem of the hyperbolic type in a Hilbert space with self-adjoint positive definite operator. Stability estimates for solution of the difference scheme are obtained. Some results of numerical experiments that support theoretical statements are presented.

scholarly journals Numerical Solution of Stochastic Hyperbolic Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Necmettin Aggez ◽  
Maral Ashyralyyewa
Keyword(s):  
Difference Scheme ◽  
Numerical Solution ◽  
Hyperbolic Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Convergence Estimate ◽  
Numerical Examples ◽  
Convergence Estimates ◽  
The Difference ◽  
Initial Boundary Value

A two-step difference scheme for the numerical solution of the initial-boundary value problem for stochastic hyperbolic equations is presented. The convergence estimate for the solution of the difference scheme is established. In applications, the convergence estimates for the solution of the difference scheme are obtained for different initialboundary value problems. The theoretical statements for the solution of this difference scheme are supported by numerical examples.

scholarly journals Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Asker Hanalyev
Keyword(s):  
Differential Equation ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Continuous Functions ◽  
Parabolic Differential Equation ◽  
Well Posedness ◽  
Nonlocal Boundary Value Problem ◽  
Hölder Condition ◽  
Linear Positive Operator

The nonlocal boundary value problem for the parabolic differential equationv'(t)+A(t)v(t)=f(t)  (0≤t≤T),  v(0)=v(λ)+φ,  0<λ≤Tin an arbitrary Banach spaceEwith the dependent linear positive operatorA(t)is investigated. The well-posedness of this problem is established in Banach spacesC0β,γ(Eα-β)of allEα-β-valued continuous functionsφ(t)on[0,T]satisfying a Hölder condition with a weight(t+τ)γ. New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.

Sign in / Sign up

Export Citation Format

Share Document