On a new class of additive (splitting) operator-difference schemes

TL;DR

This paper introduces a new class of additive operator-difference schemes for time-dependent problems with additive operators, focusing on vector schemes that transition from single equations to systems for improved solution methods.

Contribution

It develops and analyzes a novel class of vector operator-difference schemes based on additive operator splitting for problems with additive operators in the time derivative.

Findings

Constructed new vector schemes for additive operator problems

Analyzed stability and convergence of the schemes

Provided a framework for solving complex time-dependent problems

Abstract

Many applied time-dependent problems are characterized by an additive representation of the problem operator. Additive schemes are constructed using such a splitting and associated with the transition to a new time level on the basis of the solution of more simple problems for the individual operators in the additive decomposition. We consider a new class of additive schemes for problems with additive representation of the operator at the time derivative. In this paper we construct and study the vector operator-difference schemes, which are characterized by a transition from one initial the evolution equation to a system of such equations.