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A unified approach to study the existence and numerical solution of functional differential equation

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Dang Quang A, Dang Quang Long

Numerical Analysis · Submitted 23 Jan 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and construct a numerical method for solving it.

how it is stated · asserted 1.00 read the record →

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arXiv ID2101.09519 (version 1)
Pith IDKZGPVNMT, Pith's permanent record of this paper and its review
CitationDang Quang A, Dang Quang Long. "A unified approach to study the existence and numerical solution of functional differential equation." arXiv:2101.09519 (2021). https://pith.science/paper/KZGPVNMT
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,112 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.92 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and construct a numerical method for solving it. We prove that the method is of second order accuracy and obtain an estimate for total error. Some examples demonstrate the validity of the obtained theoretical results and the efficiency of the numerical method. The approach used for the third order nonlinear functional differential equation can be applied to functional differential equations of any orders.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. background 0.73 0.67 0.03 asserted 0.87
s1 By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and construct a numerical method for solving it. contribution 0.72 0.96 0.55 asserted 1.00
s2 We prove that the method is of second order accuracy and obtain an estimate for total error. result 0.94 0.96 0.17 asserted 1.00
s3 Some examples demonstrate the validity of the obtained theoretical results and the efficiency of the numerical method. result 0.80 0.95 0.13 asserted 1.00
s4 The approach used for the third order nonlinear functional differential equation can be applied to functional differential equations of any orders. interpretation 0.83 0.51 0.26 asserted 0.95

What kind of paper the classifier reports this is: method or tool 0.63 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read
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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and construct a numerical method for solving it. We prove that the method is of second order accuracy and obtain an estimate for total error. Some examples demonstrate the validity of the obtained theoretical results and the efficiency of the numerical method. The approach used for the third order nonlinear functional differential equation can be applied to functional differential equations of any orders.

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