Reduction of A Three-Layer Semi-Discrete Scheme for an Abstract Parabolic Equation to Two-Layer Schemes. Explicit Estimates for the Approximate Solution Error

2015 ◽  
Vol 206 (4) ◽  
pp. 424-444
Author(s):  
J. Rogava ◽  
D. Gulua
Keyword(s):  
Approximate Solution ◽  
Parabolic Equation ◽  
Discrete Scheme ◽  
Abstract Parabolic Equation

The perturbation algorithm for the realization of a four-layer semi-discrete solution scheme of an abstract evolutionary problem

2018 ◽  
Vol 25 (1) ◽  
pp. 77-92
Author(s):  
Jemal Rogava ◽  
David Gulua
Keyword(s):  
Hilbert Space ◽  
Approximate Solution ◽  
Original Problem ◽  
Evolutionary Equation ◽  
Discrete Solution ◽  
Discrete Scheme ◽  
Evolutionary Problem ◽  
Solution Scheme

AbstractIn the present paper, we use the perturbation algorithm to reduce a purely implicit four-layer semi-discrete scheme for an abstract evolutionary equation to two-layer schemes. An approximate solution of the original problem is constructed using the solutions of these schemes. Estimates of the approximate solution error are proved in a Hilbert space.

ON THE CONVERGENCE AND RATE OF THE CONVERGENCE OF A PROJECTION-DIFFERENCE METHOD FOR APPROXIMATE SOLVING A PARABOLIC EQUATION WITH WEIGHT INTEGRAL CONDITION

2018 ◽  
pp. 517-523
Author(s):  
Anastasiya Alexandrovna Petrova
Keyword(s):  
Finite Element Method ◽  
Hilbert Space ◽  
Approximate Solution ◽  
Parabolic Equation ◽  
Integral Condition ◽  
Approximate Solutions ◽  
Linear Parabolic Equation ◽  
The Finite Element Method ◽  
Spatial Variables ◽  
Euler’S Method

In the Hilbert space the abstract linear parabolic equation with nonlocal weight integral condition for the solution is resolved approximately by projectiondifference method using time-implicit Euler’s method. Approximation of the problem by spatial variables is oriented on the finite element method. Errors estimations of approximate solutions, convergence of approximate solution to exact one and orders of rate of convergence are established.

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