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

Author: Jemal Rogava
Co-authors: David Gulua
Keywords: Abstract Parabolic Equation, Semi-discrete Scheme, Explicit Estimate
Annotation:

A purely implicit three-layer semi-discrete approximation scheme of second order is considered for an approximate solution of the Cauchy problem for an abstract parabolic equation. Using the perturbation algorithm this scheme is reduced to two two-layer schemes. The solutions of these schemes are used to construct an approximate solution of the initial problem. Explicit estimates for the approximate solution error are proved using the properties of a semi-group.

Lecture files:

Reduction of a Three-Layer Semi-Discrete Scheme for an Abstract Parabolic Equation to Two-Layer Schemes. Explicit Estimates of the Approximate Solution Error [en]
აბსტრაქტული პარაბოლური განტოლებისთვის სამშრიანი ნახევრადდისკრეტული სქემის მიყვანა ორშრიან სქემაზე და ცხადი შეფასებები მიახლოებითი ამონახსნის ცდომილებისთვის [ka]