Work

A numerical method without accuracy saturation for a fractional-order evolution equation in a Banach space

Year: 2025

Type: article

Abstract: We study an initial-value problem for a fractional-order evolution equation involving a strongly positive operator in a Banach space. A numerical method free from accuracy saturation is developed and justified for both the homogeneous and inhomogeneous cases. The approach is based on applying the Cayley transform to the operator coefficient and approximating the solution operator by a partial sum of its defining series. A detailed analysis reveals a power-type convergence rate that depends automatically on the smoothness of the input data.

Source: Journal of Applied and Numerical Analysis

DOI: 10.30970/ana.2025.3.102

Authors: Volodymyr Makarov, Nataliya Mayko, Vyacheslav Ryabichev

Institutions: National Academy of Sciences of Ukraine, Institute of Mathematics, Taras Shevchenko National University of Kyiv

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4414227135

FWCI: 1.529

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Cited by: 2

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