Pub Date : 2024-07-16DOI: 10.1108/ajms-09-2023-0023
Nadia El Amri, Imed Boudabbous, Mouna Yaich
PurposeThe present work focuses on the primality and the Cartesian product of graphs.Design/methodology/approachGiven a graph G, a subset M of V (G) is a module of G if, for a, b ∈ M and x ∈ V (G) M, xa ∈ E(G) if and only if xb ∈ E(G). A graph G with at least three vertices is prime if the empty set, the single-vertex sets and V (G) are the only modules of G.FindingsMotivated by works obtained on “the Cartesian product of graphs” and “the primality,” this paper creates a link between the two notions.Originality/valueIn fact, we study the primality of the Cartesian product of two connected graphs minus k vertices, where k ∈ {0, 1, 2}.
设计/方法/途径给定一个图 G，如果对于 a、b ∈ M 和 x ∈ V (G) M，当且仅当 xb ∈ E(G)时，xa∈E(G)，则 V (G) 的子集 M 是 G 的模块。如果空集、单顶点集和 V (G) 是 G 的唯一模块，则至少有三个顶点的图 G 是素数。研究结果本文受有关 "图的笛卡尔积 "和 "素数 "的研究成果的启发，在这两个概念之间建立了联系。
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Pub Date : 2024-03-21DOI: 10.1108/ajms-08-2023-0002
H. Khedhiri, Taher Mkademi
PurposeIn this paper we talk about complex matrix quaternions (biquaternions) and we deal with some abstract methods in mathematical complex matrix analysis.Design/methodology/approachWe introduce and investigate the complex space HC consisting of all 2 × 2 complex matrices of the form ξ=z1+iw1z2+iw2−z‾2−iw‾2z‾1+iw‾1, (z1,w1,z2,w2)∈C4.
目的本文讨论复矩阵四元数（双四元数），并涉及数学复矩阵分析中的一些抽象方法。设计/方法/途径我们引入并研究由所有形式为ξ=z1+w1z2+w2-z‾2-w2-z‾1+w2-z‾1+w2-1, (z1,w1,z2,w2)∈C4的 2 × 2 复矩阵组成的复空间 HC。发现我们在 HC 上发展了一种新的矩阵全纯结构，并为其提供了基本的运算微积分性质。原创性/价值我们用考奇-黎曼型四元微分方程给出了一个复矩阵变量的函数ξ∈HC 的全纯性的充分和必要条件。特别是，我们证明我们有很多一个矩阵四元变量的全态函数。
{"title":"Foundational aspects of a new matrix holomorphic structure","authors":"H. Khedhiri, Taher Mkademi","doi":"10.1108/ajms-08-2023-0002","DOIUrl":"https://doi.org/10.1108/ajms-08-2023-0002","url":null,"abstract":"<jats:sec><jats:title content-type=\"abstract-subheading\">Purpose</jats:title><jats:p>In this paper we talk about complex matrix quaternions (biquaternions) and we deal with some abstract methods in mathematical complex matrix analysis.</jats:p></jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Design/methodology/approach</jats:title><jats:p>We introduce and investigate the complex space <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:msub><m:mrow><m:mi mathvariant=\"double-struck\">H</m:mi></m:mrow><m:mrow><m:mi mathvariant=\"double-struck\">C</m:mi></m:mrow></m:msub></m:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"AJMS-08-2023-0002001.tif\" /></jats:inline-formula> consisting of all 2 × 2 complex matrices of the form <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mspace width=\"0.28em\" /><m:mi>ξ</m:mi><m:mo>=</m:mo><m:mfenced open=\"(\" close=\")\"><m:mrow><m:mtable class=\"matrix\"><m:mtr><m:mtd columnalign=\"center\"><m:msub><m:mrow><m:mi>z</m:mi></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow></m:msub><m:mo>+</m:mo><m:mi>i</m:mi><m:msub><m:mrow><m:mi>w</m:mi></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow></m:msub></m:mtd><m:mtd columnalign=\"center\"><m:msub><m:mrow><m:mi>z</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow></m:msub><m:mo>+</m:mo><m:mi>i</m:mi><m:msub><m:mrow><m:mi>w</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow></m:msub></m:mtd></m:mtr><m:mtr><m:mtd columnalign=\"center\"><m:mo>−</m:mo><m:msub><m:mrow><m:mover accent=\"true\"><m:mrow><m:mi>z</m:mi></m:mrow><m:mo>‾</m:mo></m:mover></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow></m:msub><m:mo>−</m:mo><m:mi>i</m:mi><m:msub><m:mrow><m:mover accent=\"true\"><m:mrow><m:mi>w</m:mi></m:mrow><m:mo>‾</m:mo></m:mover></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow></m:msub></m:mtd><m:mtd columnalign=\"center\"><m:msub><m:mrow><m:mover accent=\"true\"><m:mrow><m:mi>z</m:mi></m:mrow><m:mo>‾</m:mo></m:mover></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow></m:msub><m:mo>+</m:mo><m:mi>i</m:mi><m:msub><m:mrow><m:mover accent=\"true\"><m:mrow><m:mi>w</m:mi></m:mrow><m:mo>‾</m:mo></m:mover></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow></m:msub></m:mtd></m:mtr></m:mtable></m:mrow></m:mfenced></m:math>, <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mrow><m:mo>(</m:mo><m:mrow><m:msub><m:mrow><m:mi>z</m:mi></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow></m:msub><m:mo>,</m:mo><m:msub><m:mrow><m:mi>w</m:mi></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow></m:msub><m:mo>,</m:mo><m:msub><m:mrow><m:mi>z</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow></m:msub><m:mo>,</m:mo><m:msub><m:mrow><m:mi>w</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow></m:msub></m:mrow><m:mo>)</m:mo></m:mrow><m:mo>∈</m:mo><m:msup><m:mrow><m:mi mathvariant=\"double-struck\">C</m:mi></m:mrow><m:mrow><m:mn>4</m:mn></m:mrow></m:msup></m:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"AJMS-08-2023-0002002.tif\" /></jats:inline-formula>.</jats:p></jats:sec><jats:sec><jats:title ","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":"86 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140223979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-18DOI: 10.1108/ajms-09-2023-0024
Hani Abidi, Rim Amami, Roger Pettersson, Chiraz Trabelsi
PurposeThe main motivation of this paper is to present the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L2-convergence rate is established.Design/methodology/approachThe authors establish a result concerning the L2-convergence rate of the solution of backward stochastic differential equation with jumps with respect to the Yosida approximation.Findings The authors carry out a convergence rate of Yosida approximation to the semi-linear backward stochastic differential equation in infinite dimension.Originality/valueIn this paper, the authors present the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L2-convergence rate is established.
{"title":"L2-convergence of Yosida approximation for semi-linear backward stochastic differential equation with jumps in infinite dimension","authors":"Hani Abidi, Rim Amami, Roger Pettersson, Chiraz Trabelsi","doi":"10.1108/ajms-09-2023-0024","DOIUrl":"https://doi.org/10.1108/ajms-09-2023-0024","url":null,"abstract":"PurposeThe main motivation of this paper is to present the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L2-convergence rate is established.Design/methodology/approachThe authors establish a result concerning the L2-convergence rate of the solution of backward stochastic differential equation with jumps with respect to the Yosida approximation.Findings The authors carry out a convergence rate of Yosida approximation to the semi-linear backward stochastic differential equation in infinite dimension.Originality/valueIn this paper, the authors present the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L2-convergence rate is established.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":"7 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139525941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-05DOI: 10.1108/ajms-08-2022-0186
Ranjitha Kumar
PurposeThe aims of this paper is to prove that every semisimple Jordan algebra bundle is locally trivial and establish the decomposition theorem for locally trivial Jordan algebra bundles using the decomposition theorem of Lie algebra bundles.Design/methodology/approachUsing the decomposition theorem of Lie algebra bundles, this paper proves the decomposition theorem for locally trivial Jordan algebra bundles.FindingsFindings of this paper establish the decomposition theorem for locally trivial Jordan algebra bundles.Originality/valueTo the best of the author’s knowledge, all the results are new and interesting to the field of Mathematics and Theoretical Physics community.
{"title":"Structure theorem for Jordan algebra bundles","authors":"Ranjitha Kumar","doi":"10.1108/ajms-08-2022-0186","DOIUrl":"https://doi.org/10.1108/ajms-08-2022-0186","url":null,"abstract":"PurposeThe aims of this paper is to prove that every semisimple Jordan algebra bundle is locally trivial and establish the decomposition theorem for locally trivial Jordan algebra bundles using the decomposition theorem of Lie algebra bundles.Design/methodology/approachUsing the decomposition theorem of Lie algebra bundles, this paper proves the decomposition theorem for locally trivial Jordan algebra bundles.FindingsFindings of this paper establish the decomposition theorem for locally trivial Jordan algebra bundles.Originality/valueTo the best of the author’s knowledge, all the results are new and interesting to the field of Mathematics and Theoretical Physics community.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45398336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-05DOI: 10.1108/ajms-10-2022-0242
E. Ballico
PurposeThe author studies forms over finite fields obtained as the determinant of Hermitian matrices and use these determinatal forms to define and study the base polynomial of a square matrix over a finite field.Design/methodology/approachThe authors give full proofs for the new results, quoting previous works by other authors in the proofs. In the introduction, the authors quoted related references.FindingsThe authors get a few theorems, mainly describing some monic polynomial arising as a base polynomial of a square matrix.Originality/valueAs far as the author knows, all the results are new, and the approach is also new.
{"title":"Determinantal polynomials and the base polynomial of a square matrix over a finite field","authors":"E. Ballico","doi":"10.1108/ajms-10-2022-0242","DOIUrl":"https://doi.org/10.1108/ajms-10-2022-0242","url":null,"abstract":"PurposeThe author studies forms over finite fields obtained as the determinant of Hermitian matrices and use these determinatal forms to define and study the base polynomial of a square matrix over a finite field.Design/methodology/approachThe authors give full proofs for the new results, quoting previous works by other authors in the proofs. In the introduction, the authors quoted related references.FindingsThe authors get a few theorems, mainly describing some monic polynomial arising as a base polynomial of a square matrix.Originality/valueAs far as the author knows, all the results are new, and the approach is also new.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43660768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-27DOI: 10.1108/ajms-04-2022-0101
L. Rakhimi, R. Daher
PurposeUsing a generalized translation operator, this study aims to obtain a generalization of Titchmarsh's theorem for the Laguerre–Bessel transform for functions satisfying the ψ-Laguerre–Bessel–Lipschitz condition in the space L2α (K), where K=0,+∞×0,+∞[.Design/methodology/approachThe author has employed the results developed by Titchmarsh, of reference number [1].FindingsIn this paper, an analogous of Titchmarsh's theorem is established for Laguerre–Bessel transform.Originality/valueTo the best of the authors’ findings, at the time of submission of this paper, the results reported are new and interesting.
{"title":"An analog of Titchmarsh's theorem for the Laguerre–Bessel transform","authors":"L. Rakhimi, R. Daher","doi":"10.1108/ajms-04-2022-0101","DOIUrl":"https://doi.org/10.1108/ajms-04-2022-0101","url":null,"abstract":"PurposeUsing a generalized translation operator, this study aims to obtain a generalization of Titchmarsh's theorem for the Laguerre–Bessel transform for functions satisfying the ψ-Laguerre–Bessel–Lipschitz condition in the space L2α (K), where K=0,+∞×0,+∞[.Design/methodology/approachThe author has employed the results developed by Titchmarsh, of reference number [1].FindingsIn this paper, an analogous of Titchmarsh's theorem is established for Laguerre–Bessel transform.Originality/valueTo the best of the authors’ findings, at the time of submission of this paper, the results reported are new and interesting.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46833100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-21DOI: 10.1108/ajms-08-2021-0174
Abdelmoumene Djabi
PurposeThe paper presents a mathematical problem involving quasistatic contact between a thermo-electro-viscoelastic body and a lubricated foundation, where the contact is described using a version of Coulomb’s law of friction that includes normal damped response conditions and heat exchange with a conductive foundation. The constitutive law for the material is thermo-electro-viscoelastic. The problem is formulated as a system that includes a parabolic equation of the first kind for the temperature, an evolutionary elliptic quasivariational inequality for the displacement and a variational elliptic equality for the electric stress. The author establishes the existence of a unique weak solution to the problem by utilizing classical results for evolutionary quasivariational elliptic inequalities, parabolic differential equations and fixed point arguments.Design/methodology/approachThe author establishes a variational formulation for the model and proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.FindingsThe author proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.Originality/valueThe author studies a mathematical problem between a thermo-electro-viscoelastic body and a lubricated foundation using a version of Coulomb’s law of friction including the normal damped response conditions and the heat exchange with a conductive foundation, which is original and requires a good understanding of modeling and mathematical tools.
{"title":"A frictional contact problem with normal damped response conditions and thermal effects for a thermo-electro-viscoelastic material","authors":"Abdelmoumene Djabi","doi":"10.1108/ajms-08-2021-0174","DOIUrl":"https://doi.org/10.1108/ajms-08-2021-0174","url":null,"abstract":"PurposeThe paper presents a mathematical problem involving quasistatic contact between a thermo-electro-viscoelastic body and a lubricated foundation, where the contact is described using a version of Coulomb’s law of friction that includes normal damped response conditions and heat exchange with a conductive foundation. The constitutive law for the material is thermo-electro-viscoelastic. The problem is formulated as a system that includes a parabolic equation of the first kind for the temperature, an evolutionary elliptic quasivariational inequality for the displacement and a variational elliptic equality for the electric stress. The author establishes the existence of a unique weak solution to the problem by utilizing classical results for evolutionary quasivariational elliptic inequalities, parabolic differential equations and fixed point arguments.Design/methodology/approachThe author establishes a variational formulation for the model and proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.FindingsThe author proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.Originality/valueThe author studies a mathematical problem between a thermo-electro-viscoelastic body and a lubricated foundation using a version of Coulomb’s law of friction including the normal damped response conditions and the heat exchange with a conductive foundation, which is original and requires a good understanding of modeling and mathematical tools.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41638317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-14DOI: 10.1108/ajms-08-2022-0195
S. Georgiev, A. Boukarou, Keltoum Bouhali, K. Zennir
PurposeThis paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.Design/methodology/approachThis paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.FindingsThis paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.Originality/valueThis article is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.
{"title":"Classical solutions for the generalized Kadomtsev–Petviashvili I equations","authors":"S. Georgiev, A. Boukarou, Keltoum Bouhali, K. Zennir","doi":"10.1108/ajms-08-2022-0195","DOIUrl":"https://doi.org/10.1108/ajms-08-2022-0195","url":null,"abstract":"PurposeThis paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.Design/methodology/approachThis paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.FindingsThis paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.Originality/valueThis article is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43580123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-28DOI: 10.1108/ajms-05-2022-0126
M.S. Daoussa Haggar, M. Mbehou
PurposeThis paper focuses on the unconditionally optimal error estimates of a linearized second-order scheme for a nonlocal nonlinear parabolic problem. The first step of the scheme is based on Crank–Nicholson method while the second step is the second-order BDF method.Design/methodology/approachA rigorous error analysis is done, and optimal L2 error estimates are derived using the error splitting technique. Some numerical simulations are presented to confirm the study’s theoretical analysis.FindingsOptimal L2 error estimates and energy norm.Originality/valueThe goal of this research article is to present and establish the unconditionally optimal error estimates of a linearized second-order BDF finite element scheme for the reaction-diffusion problem. An optimal error estimate for the proposed methods is derived by using the temporal-spatial error splitting techniques, which split the error between the exact solution and the numerical solution into two parts, that is, the temporal error and the spatial error. Since the spatial error is not dependent on the time step, the boundedness of the numerical solution in L∞-norm follows an inverse inequality immediately without any restriction on the grid mesh.
{"title":"Optimal error estimates of a linearized second-order BDF scheme for a nonlocal parabolic problem","authors":"M.S. Daoussa Haggar, M. Mbehou","doi":"10.1108/ajms-05-2022-0126","DOIUrl":"https://doi.org/10.1108/ajms-05-2022-0126","url":null,"abstract":"PurposeThis paper focuses on the unconditionally optimal error estimates of a linearized second-order scheme for a nonlocal nonlinear parabolic problem. The first step of the scheme is based on Crank–Nicholson method while the second step is the second-order BDF method.Design/methodology/approachA rigorous error analysis is done, and optimal L2 error estimates are derived using the error splitting technique. Some numerical simulations are presented to confirm the study’s theoretical analysis.FindingsOptimal L2 error estimates and energy norm.Originality/valueThe goal of this research article is to present and establish the unconditionally optimal error estimates of a linearized second-order BDF finite element scheme for the reaction-diffusion problem. An optimal error estimate for the proposed methods is derived by using the temporal-spatial error splitting techniques, which split the error between the exact solution and the numerical solution into two parts, that is, the temporal error and the spatial error. Since the spatial error is not dependent on the time step, the boundedness of the numerical solution in L∞-norm follows an inverse inequality immediately without any restriction on the grid mesh.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46378772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-28DOI: 10.1108/ajms-03-2022-0052
N. Mohdeb
PurposeIn this article, the author discusses dynamical behaviors of a prey-predator population model with nonlinear harvesting rate and offers a mathematical analysis of the model.Design/methodology/approachThe design is by using modelization of populations interaction, qualitative theory of ordinary différential equations, bifurcations analysis, invariant center manifolds theory and Dulac's criterion.FindingsThe author studies the stability of solutions and the existence of periodic solutions in the model, and proves the existence of some invariant sets and the production of a transcritical together with a saddle-node bifurcation.Practical implicationsThe author studies the effects of harvesting on the persistence and extinction properties and its influence in the perspectives of economic views.Originality/valueThe authors considers a predator–prey model with a new nonlinear form of harvesting rate. The author’s intention is to make conceptual adjustments to a well-known predator–prey model in order to incorporate the effects of harvesting.
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