Error analysis of an L2-type method on graded meshes for semilinear subdiffusion equations

Natalia Kopteva

doi:10.1016/j.aml.2024.109306

Error analysis of an L2-type method on graded meshes for semilinear subdiffusion equations

Natalia Kopteva

Research output: Contribution to journal › Article › peer-review

Abstract

A semilinear initial–boundary value problem with a Caputo time derivative of fractional order α∈(0,1) is considered, solutions of which typically exhibit a singular behaviour at an initial time. For an L2-type discretization of order 3−α, we give sharp pointwise-in-time error bounds on graded temporal meshes with arbitrary degree of grading.

Original language	English
Article number	109306
Journal	Applied Mathematics Letters
Volume	160
DOIs	https://doi.org/10.1016/j.aml.2024.109306
Publication status	Published - Feb 2025

Keywords

Graded temporal mesh
L2 scheme
Pointwise-in-time error bounds
Semilinear
Subdiffusion equation

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10.1016/j.aml.2024.109306

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title = "Error analysis of an L2-type method on graded meshes for semilinear subdiffusion equations",

abstract = "A semilinear initial–boundary value problem with a Caputo time derivative of fractional order α∈(0,1) is considered, solutions of which typically exhibit a singular behaviour at an initial time. For an L2-type discretization of order 3−α, we give sharp pointwise-in-time error bounds on graded temporal meshes with arbitrary degree of grading.",

keywords = "Graded temporal mesh, L2 scheme, Pointwise-in-time error bounds, Semilinear, Subdiffusion equation",

author = "Natalia Kopteva",

note = "Publisher Copyright: {\textcopyright} 2024 The Author(s)",

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language = "English",

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AB - A semilinear initial–boundary value problem with a Caputo time derivative of fractional order α∈(0,1) is considered, solutions of which typically exhibit a singular behaviour at an initial time. For an L2-type discretization of order 3−α, we give sharp pointwise-in-time error bounds on graded temporal meshes with arbitrary degree of grading.

KW - Graded temporal mesh

KW - L2 scheme

KW - Pointwise-in-time error bounds

KW - Semilinear

KW - Subdiffusion equation

UR - https://www.scopus.com/pages/publications/85203422890

U2 - 10.1016/j.aml.2024.109306

DO - 10.1016/j.aml.2024.109306

M3 - Article

AN - SCOPUS:85203422890

SN - 0893-9659

VL - 160

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

M1 - 109306

ER -

Error analysis of an L2-type method on graded meshes for semilinear subdiffusion equations

Abstract

Keywords

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