Pub Date : 2024-09-19DOI: 10.1186/s13661-024-01912-9
Gabriel Samaila, Basant K. Jha
The analysis of a laminar boundary layer flow near a vertical plate governed by highly nonlinear thermal radiation and chemical reaction is presented. The Boussinesq approximation is used to predict the nonlinear nature of density variation with temperature and concentration. The plate surface was subjected to the convective surface boundary condition. The partial differential equations relevant to the fluid flow was converted to ordinary differential equations, which were solved using the Runge–Kutta method after employing the shooting procedure. Some major findings are that the radiative heat flux increases the thermal energy within the boundary layer and thereby reduces the fluid viscosity, which gives rise to the velocity profile. At higher chemical reaction applications, the momentum and concentration boundary layer thickness become thinner, whereas thicker for thermal boundary layer. The rate at which the fluid reverses within the boundary increases with chemical reaction parameter. Moreover, the rate of mass transfer within the boundary layer is enhanced with chemical reaction parameters, but the contrary is true for heat transfer from the plate surface into the free stream region. There is an observable increase in the reversible fluid flow within the boundary layer for higher nonlinear density variation with temperature and concentration.
{"title":"On the combined effects of chemical reaction and nonlinear thermal radiation on natural convection heat and mass transfer over a vertical plate","authors":"Gabriel Samaila, Basant K. Jha","doi":"10.1186/s13661-024-01912-9","DOIUrl":"https://doi.org/10.1186/s13661-024-01912-9","url":null,"abstract":"The analysis of a laminar boundary layer flow near a vertical plate governed by highly nonlinear thermal radiation and chemical reaction is presented. The Boussinesq approximation is used to predict the nonlinear nature of density variation with temperature and concentration. The plate surface was subjected to the convective surface boundary condition. The partial differential equations relevant to the fluid flow was converted to ordinary differential equations, which were solved using the Runge–Kutta method after employing the shooting procedure. Some major findings are that the radiative heat flux increases the thermal energy within the boundary layer and thereby reduces the fluid viscosity, which gives rise to the velocity profile. At higher chemical reaction applications, the momentum and concentration boundary layer thickness become thinner, whereas thicker for thermal boundary layer. The rate at which the fluid reverses within the boundary increases with chemical reaction parameter. Moreover, the rate of mass transfer within the boundary layer is enhanced with chemical reaction parameters, but the contrary is true for heat transfer from the plate surface into the free stream region. There is an observable increase in the reversible fluid flow within the boundary layer for higher nonlinear density variation with temperature and concentration.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-16DOI: 10.1186/s13661-024-01925-4
Noorah Mshary, Hamdy M. Ahmed, Ahmed S. Ghanem
One of the core concepts of contemporary control theory is the idea that a dynamical system can be controlled. Several abstract settings have been developed to describe the distributed control systems in a domain in which the control is acted through the boundary. In this manuscript, we investigate the boundary approximate controllability (ABC) of stochastic differential inclusion (SDI) with Hilfer fractional derivative (HFD) and nonlocal condition by implementing the principle of stochastic analysis, the fixed-point theorem, fractional calculus and multi-valued map. Moreover, an example is offered to define the primary results.
{"title":"Effects of fractional derivative and Wiener process on approximate boundary controllability of differential inclusion","authors":"Noorah Mshary, Hamdy M. Ahmed, Ahmed S. Ghanem","doi":"10.1186/s13661-024-01925-4","DOIUrl":"https://doi.org/10.1186/s13661-024-01925-4","url":null,"abstract":"One of the core concepts of contemporary control theory is the idea that a dynamical system can be controlled. Several abstract settings have been developed to describe the distributed control systems in a domain in which the control is acted through the boundary. In this manuscript, we investigate the boundary approximate controllability (ABC) of stochastic differential inclusion (SDI) with Hilfer fractional derivative (HFD) and nonlocal condition by implementing the principle of stochastic analysis, the fixed-point theorem, fractional calculus and multi-valued map. Moreover, an example is offered to define the primary results.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-12DOI: 10.1186/s13661-024-01924-5
Chahinez Bellamouchi, Mohamed Karim Hamdani, Salah Boulaaras
In this paper, we prove that under weak assumptions on the reaction terms and diffusion coefficients, a positive solution exists for a one-dimensional case and a positive radial solution to a multidimensional case of a nonlocal elliptic problem. Additionally, we establish the uniqueness of the solution, with the fixed point theorem being the primary tool employed. Our results are new and generalize several existing results.
{"title":"Existence and uniqueness of positive solution to a new class of nonlocal elliptic problem with parameter dependency","authors":"Chahinez Bellamouchi, Mohamed Karim Hamdani, Salah Boulaaras","doi":"10.1186/s13661-024-01924-5","DOIUrl":"https://doi.org/10.1186/s13661-024-01924-5","url":null,"abstract":"In this paper, we prove that under weak assumptions on the reaction terms and diffusion coefficients, a positive solution exists for a one-dimensional case and a positive radial solution to a multidimensional case of a nonlocal elliptic problem. Additionally, we establish the uniqueness of the solution, with the fixed point theorem being the primary tool employed. Our results are new and generalize several existing results.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The current paper undertakes an in-depth exploration of the dynamics of nonlinear waves governed by a 3D-modified nonlinear wave equation, a significant model in the study of complex wave phenomena. To this end, the study employs both classical and nonclassical Lie symmetries for rigorously deriving invariant solutions of the governing equation. These symmetries enable the formal construction of exact solutions, which are crucial for understanding the complex behavior of the model. Furthermore, the research extends into the realm of bifurcation analysis through the application of planar dynamical system theory. Such an analysis reveals the conditions under which the 3D-modified nonlinear wave equation admits Jacobi elliptic function solutions. The study also delves into the impact of the nonlinear parameter on the physical characteristics of bright and kink solitary waves as well as continuous periodic waves using Maple. Overall, the comprehensive analysis presented not only enhances the understanding of complex nonlinear wave dynamics but also sets the stage for future advancements in vast areas of fluid dynamics and plasma physics.
本文深入探讨了由三维修正非线性波方程支配的非线性波的动力学，该方程是研究复杂波现象的一个重要模型。为此，研究采用了经典和非经典的李对称性来严格推导支配方程的不变解。这些对称性使得精确解的正式构建成为可能，而精确解对于理解模型的复杂行为至关重要。此外，研究还通过平面动力系统理论的应用扩展到了分岔分析领域。这种分析揭示了三维修正非线性波方程接受雅可比椭圆函数解的条件。研究还利用 Maple 深入探讨了非线性参数对亮波和扭结孤波以及连续周期波物理特性的影响。总之，所做的全面分析不仅增强了人们对复杂非线性波动力学的理解，还为未来在流体动力学和等离子体物理学的广泛领域取得进展奠定了基础。
{"title":"Classical and nonclassical Lie symmetries, bifurcation analysis, and Jacobi elliptic function solutions to a 3D-modified nonlinear wave equation in liquid involving gas bubbles","authors":"Farzaneh Alizadeh, Kamyar Hosseini, Sekson Sirisubtawee, Evren Hincal","doi":"10.1186/s13661-024-01921-8","DOIUrl":"https://doi.org/10.1186/s13661-024-01921-8","url":null,"abstract":"The current paper undertakes an in-depth exploration of the dynamics of nonlinear waves governed by a 3D-modified nonlinear wave equation, a significant model in the study of complex wave phenomena. To this end, the study employs both classical and nonclassical Lie symmetries for rigorously deriving invariant solutions of the governing equation. These symmetries enable the formal construction of exact solutions, which are crucial for understanding the complex behavior of the model. Furthermore, the research extends into the realm of bifurcation analysis through the application of planar dynamical system theory. Such an analysis reveals the conditions under which the 3D-modified nonlinear wave equation admits Jacobi elliptic function solutions. The study also delves into the impact of the nonlinear parameter on the physical characteristics of bright and kink solitary waves as well as continuous periodic waves using Maple. Overall, the comprehensive analysis presented not only enhances the understanding of complex nonlinear wave dynamics but also sets the stage for future advancements in vast areas of fluid dynamics and plasma physics.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-12DOI: 10.1186/s13661-024-01918-3
HuiYan Cheng, Naila, Akbar Zada, Ioan-Lucian Popa, Afef Kallekh
The primary objective of this manuscript is to investigate the existence and uniqueness of solutions for the Langevin $(mathtt{k},varphi )$ -Hilfer fractional differential equation of different orders with multipoint nonlocal fractional integral boundary conditions. We consider the generalized version of the Hilfer fractional diferential equation called as $(mathtt{k},varphi )$ -Hilfer fractional differential equation. We provide some significant outcomes about $(mathtt{k},varphi )$ -Hilfer fractional Langevin differential equation that requires deriving equivalent fractional integral equation to $(mathtt{k},varphi )$ -Hilfer Langevin fractional differential equation. The existence result is established using the Krasnoselskii’s fixed-point theorem, while the uniqueness is addressed with the help of Banach contraction principle. Additionally, we investigate the different forms of Ulam stability for the solution of the mentioned problem, under specific conditions. To validate our main outcomes, we present a detailed example at the end of the manuscript.
{"title":"((mathtt{k},varphi ))-Hilfer fractional Langevin differential equation having multipoint boundary conditions","authors":"HuiYan Cheng, Naila, Akbar Zada, Ioan-Lucian Popa, Afef Kallekh","doi":"10.1186/s13661-024-01918-3","DOIUrl":"https://doi.org/10.1186/s13661-024-01918-3","url":null,"abstract":"The primary objective of this manuscript is to investigate the existence and uniqueness of solutions for the Langevin $(mathtt{k},varphi )$ -Hilfer fractional differential equation of different orders with multipoint nonlocal fractional integral boundary conditions. We consider the generalized version of the Hilfer fractional diferential equation called as $(mathtt{k},varphi )$ -Hilfer fractional differential equation. We provide some significant outcomes about $(mathtt{k},varphi )$ -Hilfer fractional Langevin differential equation that requires deriving equivalent fractional integral equation to $(mathtt{k},varphi )$ -Hilfer Langevin fractional differential equation. The existence result is established using the Krasnoselskii’s fixed-point theorem, while the uniqueness is addressed with the help of Banach contraction principle. Additionally, we investigate the different forms of Ulam stability for the solution of the mentioned problem, under specific conditions. To validate our main outcomes, we present a detailed example at the end of the manuscript.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-11DOI: 10.1186/s13661-024-01920-9
Hamid Reza Sahebi, Manochehr Kazemi, Mohammad Esmael Samei
The paper focuses on establishing sufficient conditions for the existence of the solutions in some functional q-integral equations, particularly in Banach spaces. In this method, the technique of measures of noncompactness and Petryshyn’s fixed point theorem in Banach space is used. We provide some examples of equations, which confirm that our result is applicable to a wide class of integral equations.
{"title":"Some existence results for a nonlinear q-integral equations via M.N.C and fixed point theorem Petryshyn","authors":"Hamid Reza Sahebi, Manochehr Kazemi, Mohammad Esmael Samei","doi":"10.1186/s13661-024-01920-9","DOIUrl":"https://doi.org/10.1186/s13661-024-01920-9","url":null,"abstract":"The paper focuses on establishing sufficient conditions for the existence of the solutions in some functional q-integral equations, particularly in Banach spaces. In this method, the technique of measures of noncompactness and Petryshyn’s fixed point theorem in Banach space is used. We provide some examples of equations, which confirm that our result is applicable to a wide class of integral equations.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-11DOI: 10.1186/s13661-024-01917-4
Guoqiang Duan, Jialin Wang, Dongni Liao
We investigate the interior regularity to nonlinear subelliptic systems in divergence form with drift term for the case of superquadratic controllable structure conditions in the Heisenberg group. On the basis of a generalization of the $mathcal{A}$ -harmonic approximation technique, $C^{1}$ -regularity is established for horizontal gradients of vector-valued solutions to the subelliptic systems with drift term. Specially, our result is optimal in the sense that in the case of Hölder continuous coefficients we directly attain the optimal Hölder exponent for the horizontal gradients of weak solutions on the regular set.
{"title":"(C^{1})-Regularity for subelliptic systems with drift in the Heisenberg group: the superquadratic controllable growth","authors":"Guoqiang Duan, Jialin Wang, Dongni Liao","doi":"10.1186/s13661-024-01917-4","DOIUrl":"https://doi.org/10.1186/s13661-024-01917-4","url":null,"abstract":"We investigate the interior regularity to nonlinear subelliptic systems in divergence form with drift term for the case of superquadratic controllable structure conditions in the Heisenberg group. On the basis of a generalization of the $mathcal{A}$ -harmonic approximation technique, $C^{1}$ -regularity is established for horizontal gradients of vector-valued solutions to the subelliptic systems with drift term. Specially, our result is optimal in the sense that in the case of Hölder continuous coefficients we directly attain the optimal Hölder exponent for the horizontal gradients of weak solutions on the regular set.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-11DOI: 10.1186/s13661-024-01919-2
Zafer Bekiryazici
In this study, an ordinary-deterministic equation system modeling the spread dynamics of malware under mutation is analyzed with fractional derivatives and random variables. The original model is transformed into a system of fractional-random differential equations (FRDEs) using Caputo fractional derivatives. Normally distributed random variables are defined for the parameters of the original system that are related to the mutations and infections of the nodes in the network. The resulting system of FRDEs is simulated using the predictor-corrector method based fde12 algorithm and the forward fractional Euler method (ffEm) for various values of the model components such as the standard deviations, orders of derivation, and repetition numbers. Additionally, the sensitivity analysis of the original model is investigated in relation to the random nature of the components and the basic reproduction number ( $R_{0}$ ) to underline the correspondence of random dynamics and sensitivity indices. Both the normalized forward sensitivity indices (NFSI) and the standard deviation of $R_{0}$ with random components give matching results for analyzing the changes in the spread rate. Theoretical results are backed by the simulation outputs on the numerical characteristics of the fractional-random model for the expected number of infections and mutations, expected timing of the removal of mutations from the network, and measurement of the variability in the results such as the coefficients of variation. Comparison of the results from the original model and the fractional-random model shows that the fractional-random analysis provides a more generalized perspective while facilitating a versatile investigation with ease and can be used on different models as well.
{"title":"Utilizing fractional derivatives and sensitivity analysis in a random framework: a model-based approach to the investigation of random dynamics of malware spread","authors":"Zafer Bekiryazici","doi":"10.1186/s13661-024-01919-2","DOIUrl":"https://doi.org/10.1186/s13661-024-01919-2","url":null,"abstract":"In this study, an ordinary-deterministic equation system modeling the spread dynamics of malware under mutation is analyzed with fractional derivatives and random variables. The original model is transformed into a system of fractional-random differential equations (FRDEs) using Caputo fractional derivatives. Normally distributed random variables are defined for the parameters of the original system that are related to the mutations and infections of the nodes in the network. The resulting system of FRDEs is simulated using the predictor-corrector method based fde12 algorithm and the forward fractional Euler method (ffEm) for various values of the model components such as the standard deviations, orders of derivation, and repetition numbers. Additionally, the sensitivity analysis of the original model is investigated in relation to the random nature of the components and the basic reproduction number ( $R_{0}$ ) to underline the correspondence of random dynamics and sensitivity indices. Both the normalized forward sensitivity indices (NFSI) and the standard deviation of $R_{0}$ with random components give matching results for analyzing the changes in the spread rate. Theoretical results are backed by the simulation outputs on the numerical characteristics of the fractional-random model for the expected number of infections and mutations, expected timing of the removal of mutations from the network, and measurement of the variability in the results such as the coefficients of variation. Comparison of the results from the original model and the fractional-random model shows that the fractional-random analysis provides a more generalized perspective while facilitating a versatile investigation with ease and can be used on different models as well.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-09DOI: 10.1186/s13661-024-01913-8
A. I. Ahmed, M. S. Al-Sharif
In this paper, the fractional-order Chelyshkov functions (FCHFs) and Riemann-Liouville fractional integrals are utilized to find numerical solutions to fractional delay differential equations, by transforming the problem into a system of algebraic equations with unknown FCHFs coefficients. An error bound of FCHFs approximation is estimated and its convergence is also demonstrated. The effectiveness and accuracy of the presented method are established through several examples. The resulting solution is accurate and agrees with the exact solution, even if the exact solution is not a polynomial. Moreover, comparisons between the obtained numerical results and those recently reported in the literature are shown.
{"title":"An effective numerical method for solving fractional delay differential equations using fractional-order Chelyshkov functions","authors":"A. I. Ahmed, M. S. Al-Sharif","doi":"10.1186/s13661-024-01913-8","DOIUrl":"https://doi.org/10.1186/s13661-024-01913-8","url":null,"abstract":"In this paper, the fractional-order Chelyshkov functions (FCHFs) and Riemann-Liouville fractional integrals are utilized to find numerical solutions to fractional delay differential equations, by transforming the problem into a system of algebraic equations with unknown FCHFs coefficients. An error bound of FCHFs approximation is estimated and its convergence is also demonstrated. The effectiveness and accuracy of the presented method are established through several examples. The resulting solution is accurate and agrees with the exact solution, even if the exact solution is not a polynomial. Moreover, comparisons between the obtained numerical results and those recently reported in the literature are shown.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-06DOI: 10.1186/s13661-024-01915-6
Man Luo, Da Xu, Xianmin Pan
In this article, a new numerical algorithm for solving a 1-dimensional (1D) and 2-dimensional (2D) time-fractional diffusion equation is proposed. The Sinc-Galerkin scheme is considered for spatial discretization, and a higher-order finite difference formula is considered for temporal discretization. The convergence behavior of the methods is analyzed, and the error bounds are provided. The main objective of this paper is to propose the error bounds for 2D problems by using the Sinc-Galerkin method. The proposed method in terms of convergence is studied by using the characteristics of the Sinc function in detail with optimal rates of exponential convergence for 2D problems. Some numerical experiments validate the theoretical results and present the efficiency of the proposed schemes.
{"title":"Sinc-Galerkin method and a higher-order method for a 1D and 2D time-fractional diffusion equations","authors":"Man Luo, Da Xu, Xianmin Pan","doi":"10.1186/s13661-024-01915-6","DOIUrl":"https://doi.org/10.1186/s13661-024-01915-6","url":null,"abstract":"In this article, a new numerical algorithm for solving a 1-dimensional (1D) and 2-dimensional (2D) time-fractional diffusion equation is proposed. The Sinc-Galerkin scheme is considered for spatial discretization, and a higher-order finite difference formula is considered for temporal discretization. The convergence behavior of the methods is analyzed, and the error bounds are provided. The main objective of this paper is to propose the error bounds for 2D problems by using the Sinc-Galerkin method. The proposed method in terms of convergence is studied by using the characteristics of the Sinc function in detail with optimal rates of exponential convergence for 2D problems. Some numerical experiments validate the theoretical results and present the efficiency of the proposed schemes.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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