Approximate solution of a parabolic equation with the use of a rational approximation to the operator exponential

2017 ◽  
Vol 53 (3) ◽  
pp. 398-408 ◽  
Author(s):  
M. N. Oreshina
Keyword(s):  
Approximate Solution ◽  
Parabolic Equation ◽  
Rational Approximation ◽  
Operator Exponential

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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