Approximation of Caputo time-fractional diffusion equation using redefined cubic exponential B-spline collocation technique Article Swipe

View

Mohammad Tamsir , Neeraj Dhiman , Deependra Nigam , Anand Chauhan ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.3934/math.2021226

The purpose of this work is to find the numerical solution of the Caputo time-fractional diffusion equation using the modified cubic exponential B-spline (CExpB-spline) collocation technique. First, the CExpB-spline functions are modified and then used to discretize the space derivatives. Three numerical examples are considered for checking the efficiency and accuracy of the method. The obtained results are compared with those reported earlier showing that the present technique gives highly accurate results. Von Neumann stability is carried out which gives the guarantee that the technique is unconditionally stable. The rate of convergence is also obtained. Furthermore, this technique is efficient and requires less storage.

Related Topics

Mathematics

Mathematical Analysis

Computer Science

Differential Equation

Bilinear Interpolation

Economy

Concepts

Discretization Mathematics Exponential function Collocation method Collocation (remote sensing) B-spline Applied mathematics Spline (mechanical) Mathematical analysis Thin plate spline Diffusion equation Spline interpolation Computer science Differential equation Physics Machine learning Economics Statistics Bilinear interpolation Thermodynamics Economy Service (business) Ordinary differential equation

Metadata

Type: article
Language: en
Landing Page: https://doi.org/10.3934/math.2021226
OA Status: gold
Cited By: 18
References: 42
Related Works: 10
OpenAlex ID: https://openalex.org/W3128088540

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W3128088540

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.3934/math.2021226

Digital Object Identifier
Title: Approximation of Caputo time-fractional diffusion equation using redefined cubic exponential B-spline collocation technique

Work title
Type: article

OpenAlex work type
Language: en

Primary language
Publication year: 2021

Year of publication
Publication date: 2021-01-01

Full publication date if available
Authors: Mohammad Tamsir, Neeraj Dhiman, Deependra Nigam, Anand Chauhan

List of authors in order
Landing page: https://doi.org/10.3934/math.2021226

Publisher landing page
Open access: Yes

Whether a free full text is available
OA status: gold

Open access status per OpenAlex
OA URL: https://doi.org/10.3934/math.2021226

Direct OA link when available
Concepts: Discretization, Mathematics, Exponential function, Collocation method, Collocation (remote sensing), B-spline, Applied mathematics, Spline (mechanical), Mathematical analysis, Thin plate spline, Diffusion equation, Spline interpolation, Computer science, Differential equation, Physics, Machine learning, Economics, Statistics, Bilinear interpolation, Thermodynamics, Economy, Service (business), Ordinary differential equation

Top concepts (fields/topics) attached by OpenAlex
Cited by: 18

Total citation count in OpenAlex
Citations by year (recent): 2025: 3, 2024: 2, 2023: 7, 2022: 2, 2021: 4

Per-year citation counts (last 5 years)
References (count): 42

Number of works referenced by this work
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W3128088540
doi	https://doi.org/10.3934/math.2021226
ids.doi	https://doi.org/10.3934/math.2021226
ids.mag	3128088540
ids.openalex	https://openalex.org/W3128088540
fwci	1.36300877
type	article
title	Approximation of Caputo time-fractional diffusion equation using redefined cubic exponential B-spline collocation technique
biblio.issue	4
biblio.volume	6
biblio.last_page	3820
biblio.first_page	3805
topics[0].id	https://openalex.org/T10288
topics[0].field.id	https://openalex.org/fields/26
topics[0].field.display_name	Mathematics
topics[0].score	1.0
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/2611
topics[0].subfield.display_name	Modeling and Simulation
topics[0].display_name	Fractional Differential Equations Solutions
topics[1].id	https://openalex.org/T10541
topics[1].field.id	https://openalex.org/fields/26
topics[1].field.display_name	Mathematics
topics[1].score	0.9919000267982483
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/2604
topics[1].subfield.display_name	Applied Mathematics
topics[1].display_name	Nonlinear Differential Equations Analysis
topics[2].id	https://openalex.org/T12727
topics[2].field.id	https://openalex.org/fields/26
topics[2].field.display_name	Mathematics
topics[2].score	0.9911999702453613
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/2612
topics[2].subfield.display_name	Numerical Analysis
topics[2].display_name	Differential Equations and Numerical Methods
is_xpac	False
apc_list.value	1200
apc_list.currency	USD
apc_list.value_usd	1200
apc_paid.value	1200
apc_paid.currency	USD
apc_paid.value_usd	1200
concepts[0].id	https://openalex.org/C73000952
concepts[0].level	2
concepts[0].score	0.7116906642913818
concepts[0].wikidata	https://www.wikidata.org/wiki/Q17007827
concepts[0].display_name	Discretization
concepts[1].id	https://openalex.org/C33923547
concepts[1].level	0
concepts[1].score	0.6635631322860718
concepts[1].wikidata	https://www.wikidata.org/wiki/Q395
concepts[1].display_name	Mathematics
concepts[2].id	https://openalex.org/C151376022
concepts[2].level	2
concepts[2].score	0.6399812698364258
concepts[2].wikidata	https://www.wikidata.org/wiki/Q168698
concepts[2].display_name	Exponential function
concepts[3].id	https://openalex.org/C2126413
concepts[3].level	4
concepts[3].score	0.6118531823158264
concepts[3].wikidata	https://www.wikidata.org/wiki/Q1779479
concepts[3].display_name	Collocation method
concepts[4].id	https://openalex.org/C80023036
concepts[4].level	2
concepts[4].score	0.49501317739486694
concepts[4].wikidata	https://www.wikidata.org/wiki/Q5147531
concepts[4].display_name	Collocation (remote sensing)
concepts[5].id	https://openalex.org/C15945459
concepts[5].level	2
concepts[5].score	0.47829920053482056
concepts[5].wikidata	https://www.wikidata.org/wiki/Q2083109
concepts[5].display_name	B-spline
concepts[6].id	https://openalex.org/C28826006
concepts[6].level	1
concepts[6].score	0.4732171595096588
concepts[6].wikidata	https://www.wikidata.org/wiki/Q33521
concepts[6].display_name	Applied mathematics
concepts[7].id	https://openalex.org/C10390562
concepts[7].level	2
concepts[7].score	0.4673628807067871
concepts[7].wikidata	https://www.wikidata.org/wiki/Q581809
concepts[7].display_name	Spline (mechanical)
concepts[8].id	https://openalex.org/C134306372
concepts[8].level	1
concepts[8].score	0.45463767647743225
concepts[8].wikidata	https://www.wikidata.org/wiki/Q7754
concepts[8].display_name	Mathematical analysis
concepts[9].id	https://openalex.org/C93132110
concepts[9].level	4
concepts[9].score	0.43795496225357056
concepts[9].wikidata	https://www.wikidata.org/wiki/Q7784288
concepts[9].display_name	Thin plate spline
concepts[10].id	https://openalex.org/C571446
concepts[10].level	3
concepts[10].score	0.4118020832538605
concepts[10].wikidata	https://www.wikidata.org/wiki/Q6510183
concepts[10].display_name	Diffusion equation
concepts[11].id	https://openalex.org/C31447003
concepts[11].level	3
concepts[11].score	0.15240105986595154
concepts[11].wikidata	https://www.wikidata.org/wiki/Q545002
concepts[11].display_name	Spline interpolation
concepts[12].id	https://openalex.org/C41008148
concepts[12].level	0
concepts[12].score	0.132045179605484
concepts[12].wikidata	https://www.wikidata.org/wiki/Q21198
concepts[12].display_name	Computer science
concepts[13].id	https://openalex.org/C78045399
concepts[13].level	2
concepts[13].score	0.11440551280975342
concepts[13].wikidata	https://www.wikidata.org/wiki/Q11214
concepts[13].display_name	Differential equation
concepts[14].id	https://openalex.org/C121332964
concepts[14].level	0
concepts[14].score	0.07462137937545776
concepts[14].wikidata	https://www.wikidata.org/wiki/Q413
concepts[14].display_name	Physics
concepts[15].id	https://openalex.org/C119857082
concepts[15].level	1
concepts[15].score	0.0
concepts[15].wikidata	https://www.wikidata.org/wiki/Q2539
concepts[15].display_name	Machine learning
concepts[16].id	https://openalex.org/C162324750
concepts[16].level	0
concepts[16].score	0.0
concepts[16].wikidata	https://www.wikidata.org/wiki/Q8134
concepts[16].display_name	Economics
concepts[17].id	https://openalex.org/C105795698
concepts[17].level	1
concepts[17].score	0.0
concepts[17].wikidata	https://www.wikidata.org/wiki/Q12483
concepts[17].display_name	Statistics
concepts[18].id	https://openalex.org/C205203396
concepts[18].level	2
concepts[18].score	0.0
concepts[18].wikidata	https://www.wikidata.org/wiki/Q612143
concepts[18].display_name	Bilinear interpolation
concepts[19].id	https://openalex.org/C97355855
concepts[19].level	1
concepts[19].score	0.0
concepts[19].wikidata	https://www.wikidata.org/wiki/Q11473
concepts[19].display_name	Thermodynamics
concepts[20].id	https://openalex.org/C136264566
concepts[20].level	1
concepts[20].score	0.0
concepts[20].wikidata	https://www.wikidata.org/wiki/Q159810
concepts[20].display_name	Economy
concepts[21].id	https://openalex.org/C2780378061
concepts[21].level	2
concepts[21].score	0.0
concepts[21].wikidata	https://www.wikidata.org/wiki/Q25351891
concepts[21].display_name	Service (business)
concepts[22].id	https://openalex.org/C51544822
concepts[22].level	3
concepts[22].score	0.0
concepts[22].wikidata	https://www.wikidata.org/wiki/Q465274
concepts[22].display_name	Ordinary differential equation
keywords[0].id	https://openalex.org/keywords/discretization
keywords[0].score	0.7116906642913818
keywords[0].display_name	Discretization
keywords[1].id	https://openalex.org/keywords/mathematics
keywords[1].score	0.6635631322860718
keywords[1].display_name	Mathematics
keywords[2].id	https://openalex.org/keywords/exponential-function
keywords[2].score	0.6399812698364258
keywords[2].display_name	Exponential function
keywords[3].id	https://openalex.org/keywords/collocation-method
keywords[3].score	0.6118531823158264
keywords[3].display_name	Collocation method
keywords[4].id	https://openalex.org/keywords/collocation
keywords[4].score	0.49501317739486694
keywords[4].display_name	Collocation (remote sensing)
keywords[5].id	https://openalex.org/keywords/b-spline
keywords[5].score	0.47829920053482056
keywords[5].display_name	B-spline
keywords[6].id	https://openalex.org/keywords/applied-mathematics
keywords[6].score	0.4732171595096588
keywords[6].display_name	Applied mathematics
keywords[7].id	https://openalex.org/keywords/spline
keywords[7].score	0.4673628807067871
keywords[7].display_name	Spline (mechanical)
keywords[8].id	https://openalex.org/keywords/mathematical-analysis
keywords[8].score	0.45463767647743225
keywords[8].display_name	Mathematical analysis
keywords[9].id	https://openalex.org/keywords/thin-plate-spline
keywords[9].score	0.43795496225357056
keywords[9].display_name	Thin plate spline
keywords[10].id	https://openalex.org/keywords/diffusion-equation
keywords[10].score	0.4118020832538605
keywords[10].display_name	Diffusion equation
keywords[11].id	https://openalex.org/keywords/spline-interpolation
keywords[11].score	0.15240105986595154
keywords[11].display_name	Spline interpolation
keywords[12].id	https://openalex.org/keywords/computer-science
keywords[12].score	0.132045179605484
keywords[12].display_name	Computer science
keywords[13].id	https://openalex.org/keywords/differential-equation
keywords[13].score	0.11440551280975342
keywords[13].display_name	Differential equation
keywords[14].id	https://openalex.org/keywords/physics
keywords[14].score	0.07462137937545776
keywords[14].display_name	Physics
language	en
locations[0].id	doi:10.3934/math.2021226
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S4210179087
locations[0].source.issn	2473-6988
locations[0].source.type	journal
locations[0].source.is_oa	True
locations[0].source.issn_l	2473-6988
locations[0].source.is_core	True
locations[0].source.is_in_doaj	True
locations[0].source.display_name	AIMS Mathematics
locations[0].source.host_organization	https://openalex.org/P4310315844
locations[0].source.host_organization_name	American Institute of Mathematical Sciences
locations[0].source.host_organization_lineage	https://openalex.org/P4310315844
locations[0].source.host_organization_lineage_names	American Institute of Mathematical Sciences
locations[0].license	cc-by
locations[0].pdf_url
locations[0].version	publishedVersion
locations[0].raw_type	journal-article
locations[0].license_id	https://openalex.org/licenses/cc-by
locations[0].is_accepted	True
locations[0].is_published	True
locations[0].raw_source_name	AIMS Mathematics
locations[0].landing_page_url	https://doi.org/10.3934/math.2021226
locations[1].id	pmh:oai:doaj.org/article:fab25a77a13746bc9c4c9b9fabd99ceb
locations[1].is_oa	True
locations[1].source.id	https://openalex.org/S4306401280
locations[1].source.issn
locations[1].source.type	repository
locations[1].source.is_oa	False
locations[1].source.issn_l
locations[1].source.is_core	False
locations[1].source.is_in_doaj	False
locations[1].source.display_name	DOAJ (DOAJ: Directory of Open Access Journals)
locations[1].source.host_organization
locations[1].source.host_organization_name
locations[1].license	cc-by-sa
locations[1].pdf_url
locations[1].version	submittedVersion
locations[1].raw_type	article
locations[1].license_id	https://openalex.org/licenses/cc-by-sa
locations[1].is_accepted	False
locations[1].is_published	False
locations[1].raw_source_name	AIMS Mathematics, Vol 6, Iss 4, Pp 3805-3820 (2021)
locations[1].landing_page_url	https://doaj.org/article/fab25a77a13746bc9c4c9b9fabd99ceb
indexed_in	crossref, doaj
authorships[0].author.id	https://openalex.org/A5012839264
authorships[0].author.orcid	https://orcid.org/0000-0002-6389-4879
authorships[0].author.display_name	Mohammad Tamsir
authorships[0].author_position	first
authorships[0].raw_author_name	Mohammad Tamsir
authorships[0].is_corresponding	False
authorships[1].author.id	https://openalex.org/A5028916525
authorships[1].author.orcid	https://orcid.org/0000-0001-5037-1537
authorships[1].author.display_name	Neeraj Dhiman
authorships[1].author_position	middle
authorships[1].raw_author_name	Neeraj Dhiman
authorships[1].is_corresponding	False
authorships[2].author.id	https://openalex.org/A5008773988
authorships[2].author.orcid	https://orcid.org/0000-0002-0403-3294
authorships[2].author.display_name	Deependra Nigam
authorships[2].author_position	middle
authorships[2].raw_author_name	Deependra Nigam
authorships[2].is_corresponding	False
authorships[3].author.id	https://openalex.org/A5025353446
authorships[3].author.orcid	https://orcid.org/0000-0002-7166-8177
authorships[3].author.display_name	Anand Chauhan
authorships[3].countries	IN, SA
authorships[3].affiliations[0].institution_ids	https://openalex.org/I60054993
authorships[3].affiliations[0].raw_affiliation_string	Department of Mathematics, Graphic Era Hill University, Dehradun, India
authorships[3].affiliations[1].institution_ids	https://openalex.org/I91450128
authorships[3].affiliations[1].raw_affiliation_string	Department of Mathematics, College of Science, Jazan University, Jazan, Saudi Arabia
authorships[3].affiliations[2].raw_affiliation_string	D. A. V. (P. G.) College, Dehradun, India
authorships[3].affiliations[3].institution_ids	https://openalex.org/I60054993
authorships[3].affiliations[3].raw_affiliation_string	Department of Mathematics, Graphic Era University, Dehradun, India
authorships[3].institutions[0].id	https://openalex.org/I60054993
authorships[3].institutions[0].ror	https://ror.org/03wqgqd89
authorships[3].institutions[0].type	education
authorships[3].institutions[0].lineage	https://openalex.org/I60054993
authorships[3].institutions[0].country_code	IN
authorships[3].institutions[0].display_name	Graphic Era University
authorships[3].institutions[1].id	https://openalex.org/I91450128
authorships[3].institutions[1].ror	https://ror.org/02bjnq803
authorships[3].institutions[1].type	education
authorships[3].institutions[1].lineage	https://openalex.org/I91450128
authorships[3].institutions[1].country_code	SA
authorships[3].institutions[1].display_name	Jazan University
authorships[3].author_position	last
authorships[3].raw_author_name	Anand Chauhan
authorships[3].is_corresponding	True
authorships[3].raw_affiliation_strings	D. A. V. (P. G.) College, Dehradun, India, Department of Mathematics, College of Science, Jazan University, Jazan, Saudi Arabia, Department of Mathematics, Graphic Era Hill University, Dehradun, India, Department of Mathematics, Graphic Era University, Dehradun, India
has_content.pdf	False
has_content.grobid_xml	False
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://doi.org/10.3934/math.2021226
open_access.oa_status	gold
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	Approximation of Caputo time-fractional diffusion equation using redefined cubic exponential B-spline collocation technique
has_fulltext	False
is_retracted	False
updated_date	2025-11-06T03:46:38.306776
primary_topic.id	https://openalex.org/T10288
primary_topic.field.id	https://openalex.org/fields/26
primary_topic.field.display_name	Mathematics
primary_topic.score	1.0
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/2611
primary_topic.subfield.display_name	Modeling and Simulation
primary_topic.display_name	Fractional Differential Equations Solutions
related_works	https://openalex.org/W2078318892, https://openalex.org/W2791210196, https://openalex.org/W1987365920, https://openalex.org/W322101810, https://openalex.org/W2384941625, https://openalex.org/W2889856026, https://openalex.org/W2009058751, https://openalex.org/W1989122168, https://openalex.org/W2131278000, https://openalex.org/W2953063785
cited_by_count	18
counts_by_year[0].year	2025
counts_by_year[0].cited_by_count	3
counts_by_year[1].year	2024
counts_by_year[1].cited_by_count	2
counts_by_year[2].year	2023
counts_by_year[2].cited_by_count	7
counts_by_year[3].year	2022
counts_by_year[3].cited_by_count	2
counts_by_year[4].year	2021
counts_by_year[4].cited_by_count	4
locations_count	2
best_oa_location.id	doi:10.3934/math.2021226
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S4210179087
best_oa_location.source.issn	2473-6988
best_oa_location.source.type	journal
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l	2473-6988
best_oa_location.source.is_core	True
best_oa_location.source.is_in_doaj	True
best_oa_location.source.display_name	AIMS Mathematics
best_oa_location.source.host_organization	https://openalex.org/P4310315844
best_oa_location.source.host_organization_name	American Institute of Mathematical Sciences
best_oa_location.source.host_organization_lineage	https://openalex.org/P4310315844
best_oa_location.source.host_organization_lineage_names	American Institute of Mathematical Sciences
best_oa_location.license	cc-by
best_oa_location.pdf_url
best_oa_location.version	publishedVersion
best_oa_location.raw_type	journal-article
best_oa_location.license_id	https://openalex.org/licenses/cc-by
best_oa_location.is_accepted	True
best_oa_location.is_published	True
best_oa_location.raw_source_name	AIMS Mathematics
best_oa_location.landing_page_url	https://doi.org/10.3934/math.2021226
primary_location.id	doi:10.3934/math.2021226
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S4210179087
primary_location.source.issn	2473-6988
primary_location.source.type	journal
primary_location.source.is_oa	True
primary_location.source.issn_l	2473-6988
primary_location.source.is_core	True
primary_location.source.is_in_doaj	True
primary_location.source.display_name	AIMS Mathematics
primary_location.source.host_organization	https://openalex.org/P4310315844
primary_location.source.host_organization_name	American Institute of Mathematical Sciences
primary_location.source.host_organization_lineage	https://openalex.org/P4310315844
primary_location.source.host_organization_lineage_names	American Institute of Mathematical Sciences
primary_location.license	cc-by
primary_location.pdf_url
primary_location.version	publishedVersion
primary_location.raw_type	journal-article
primary_location.license_id	https://openalex.org/licenses/cc-by
primary_location.is_accepted	True
primary_location.is_published	True
primary_location.raw_source_name	AIMS Mathematics
primary_location.landing_page_url	https://doi.org/10.3934/math.2021226
publication_date	2021-01-01
publication_year	2021
referenced_works	https://openalex.org/W2609268354, https://openalex.org/W2083559699, https://openalex.org/W2055148154, https://openalex.org/W2072593874, https://openalex.org/W2033275894, https://openalex.org/W2045231411, https://openalex.org/W3008547590, https://openalex.org/W1992429301, https://openalex.org/W2068563785, https://openalex.org/W2046579020, https://openalex.org/W2199368408, https://openalex.org/W2725097749, https://openalex.org/W2954754862, https://openalex.org/W2057127233, https://openalex.org/W2165076033, https://openalex.org/W2732661672, https://openalex.org/W2016755336, https://openalex.org/W2800851141, https://openalex.org/W1993748522, https://openalex.org/W1966258563, https://openalex.org/W2325298721, https://openalex.org/W2001203502, https://openalex.org/W2974787634, https://openalex.org/W2339657375, https://openalex.org/W2950965409, https://openalex.org/W2105723279, https://openalex.org/W2615849129, https://openalex.org/W2588394688, https://openalex.org/W2769471692, https://openalex.org/W2136735217, https://openalex.org/W1972900338, https://openalex.org/W2958141510, https://openalex.org/W2895510777, https://openalex.org/W2268042093, https://openalex.org/W2071861749, https://openalex.org/W2041202720, https://openalex.org/W1186992553, https://openalex.org/W1850511188, https://openalex.org/W1528987510, https://openalex.org/W4301223505, https://openalex.org/W2787959293, https://openalex.org/W2188190988
referenced_works_count	42
abstract_inverted_index.is	5, 75, 85, 92, 98
abstract_inverted_index.of	2, 11, 51, 90
abstract_inverted_index.to	6, 35
abstract_inverted_index.The	0, 54, 88
abstract_inverted_index.Von	72
abstract_inverted_index.and	32, 49, 100
abstract_inverted_index.are	30, 43, 57
abstract_inverted_index.for	45
abstract_inverted_index.out	77
abstract_inverted_index.the	8, 12, 18, 27, 37, 47, 52, 65, 80, 83
abstract_inverted_index.also	93
abstract_inverted_index.find	7
abstract_inverted_index.less	102
abstract_inverted_index.rate	89
abstract_inverted_index.that	64, 82
abstract_inverted_index.then	33
abstract_inverted_index.this	3, 96
abstract_inverted_index.used	34
abstract_inverted_index.with	59
abstract_inverted_index.work	4
abstract_inverted_index.Three	40
abstract_inverted_index.cubic	20
abstract_inverted_index.gives	68, 79
abstract_inverted_index.space	38
abstract_inverted_index.those	60
abstract_inverted_index.using	17
abstract_inverted_index.which	78
abstract_inverted_index.Caputo	13
abstract_inverted_index.First,	26
abstract_inverted_index.highly	69
abstract_inverted_index.Neumann	73
abstract_inverted_index.carried	76
abstract_inverted_index.earlier	62
abstract_inverted_index.method.	53
abstract_inverted_index.present	66
abstract_inverted_index.purpose	1
abstract_inverted_index.results	56
abstract_inverted_index.showing	63
abstract_inverted_index.stable.	87
abstract_inverted_index.B-spline	22
abstract_inverted_index.accuracy	50
abstract_inverted_index.accurate	70
abstract_inverted_index.checking	46
abstract_inverted_index.compared	58
abstract_inverted_index.equation	16
abstract_inverted_index.examples	42
abstract_inverted_index.modified	19, 31
abstract_inverted_index.obtained	55
abstract_inverted_index.reported	61
abstract_inverted_index.requires	101
abstract_inverted_index.results.	71
abstract_inverted_index.solution	10
abstract_inverted_index.storage.	103
abstract_inverted_index.diffusion	15
abstract_inverted_index.efficient	99
abstract_inverted_index.functions	29
abstract_inverted_index.guarantee	81
abstract_inverted_index.numerical	9, 41
abstract_inverted_index.obtained.	94
abstract_inverted_index.stability	74
abstract_inverted_index.technique	67, 84, 97
abstract_inverted_index.considered	44
abstract_inverted_index.discretize	36
abstract_inverted_index.efficiency	48
abstract_inverted_index.technique.	25
abstract_inverted_index.collocation	24
abstract_inverted_index.convergence	91
abstract_inverted_index.exponential	21
abstract_inverted_index.CExpB-spline	28
abstract_inverted_index.Furthermore,	95
abstract_inverted_index.derivatives.	39
abstract_inverted_index.(CExpB-spline)	23
abstract_inverted_index.time-fractional	14
abstract_inverted_index.unconditionally	86
cited_by_percentile_year.max	99
cited_by_percentile_year.min	94
corresponding_author_ids	https://openalex.org/A5025353446
countries_distinct_count	2
institutions_distinct_count	4
corresponding_institution_ids	https://openalex.org/I60054993, https://openalex.org/I91450128
citation_normalized_percentile.value	0.81305335
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	False