Pub Date : 2022-09-19DOI: 10.1515/ijnsns-2021-0459
Duong Viet Thong, Xiao-Huan Li, Q. Dong, Hoang Van Thang, Luong Van Long
Abstract The projection technique is a very important method and efficient for solving variational inequality problems. In this study, we developed the subgradient extragradient method for solving pseudomonotone variational inequality in real Hilbert spaces. Our first algorithm requires only computing one projection onto the feasible set per iteration and the strong convergence is proved without the prior knowledge of the Lipschitz constant as well as the sequentially weak continuity of the associated mapping. The second algorithm uses the linesearch procedure such that its convergence does not require the Lipschitz continuous condition of the variational inequality mapping. Finally, some numerical experiments are provided to demonstrate the advantages and efficiency of the proposed methods.
{"title":"Adaptive extragradient methods for solving variational inequalities in real Hilbert spaces","authors":"Duong Viet Thong, Xiao-Huan Li, Q. Dong, Hoang Van Thang, Luong Van Long","doi":"10.1515/ijnsns-2021-0459","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0459","url":null,"abstract":"Abstract The projection technique is a very important method and efficient for solving variational inequality problems. In this study, we developed the subgradient extragradient method for solving pseudomonotone variational inequality in real Hilbert spaces. Our first algorithm requires only computing one projection onto the feasible set per iteration and the strong convergence is proved without the prior knowledge of the Lipschitz constant as well as the sequentially weak continuity of the associated mapping. The second algorithm uses the linesearch procedure such that its convergence does not require the Lipschitz continuous condition of the variational inequality mapping. Finally, some numerical experiments are provided to demonstrate the advantages and efficiency of the proposed methods.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47613052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-19DOI: 10.1515/ijnsns-2021-0186
L. Zhang, Pengyan Liu
Abstract Recently, propagation models of worms in the mobile environment are drawing extensive attention, particularly in the Wi-Fi scenario. Considering that worm-free equilibrium is exponential convergent means that the propagation time and control time of worms are much shorter than for other asymptotic convergence. Besides, the global asymptotic stability of the endemic equilibrium is more important than the local asymptotic stability, which reflects the more global qualitative behavior of the worm propagation. In this paper, we discuss the global dynamics of SEIQR worm propagation model in mobile internet proposed by Xiao et al. [X. Xiao, P. Fu, C. Dou, Q. Li, G. Hu, and S. Xia, “Design and analysis of SEIQR worm propagation model in mobile internet,” Commun. Nonlinear Sci. Numer. Simulat., vol. 43, pp. 341–350, 2017] to improve and complement the related results. Through a series of mathematical derivations, sufficient conditions are derived to ensure the global exponentially stability of worm-free equilibrium, and the exponential convergent rate can be unveiled. Then, by using the classical geometric approach, it is shown that the endemic equilibrium is globally asymptotically stable and the system is persistent when R 0 > 1. Moreover, numerical simulations are given to demonstrate our theoretical results.
近年来，蠕虫在移动环境下的传播模式受到了广泛关注，尤其是在Wi-Fi场景下。考虑无虫平衡是指数收敛的，意味着蠕虫的传播时间和控制时间比其他渐近收敛的情况要短得多。此外，地方性平衡的全局渐近稳定性比局部渐近稳定性更重要，反映了蠕虫传播的全局定性行为。本文讨论了Xiao等人提出的移动互联网中SEIQR蠕虫传播模型的全局动态。肖平，傅平，窦晨，李强，胡国光，夏生，“移动互联网中SEIQR蠕虫传播模型的设计与分析”，通信学报。非线性科学。号码。装病者。[中文]，vol. 43, pp. 341-350, 2017]以完善和补充相关结果。通过一系列数学推导，得到了保证无虫平衡全局指数稳定的充分条件，并揭示了指数收敛速率。然后，利用经典的几何方法，证明了当R为0时，系统的局部平衡点是全局渐近稳定的，系统是持久的。通过数值模拟验证了理论结果。
{"title":"Global stability for a SEIQR worm propagation model in mobile internet","authors":"L. Zhang, Pengyan Liu","doi":"10.1515/ijnsns-2021-0186","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0186","url":null,"abstract":"Abstract Recently, propagation models of worms in the mobile environment are drawing extensive attention, particularly in the Wi-Fi scenario. Considering that worm-free equilibrium is exponential convergent means that the propagation time and control time of worms are much shorter than for other asymptotic convergence. Besides, the global asymptotic stability of the endemic equilibrium is more important than the local asymptotic stability, which reflects the more global qualitative behavior of the worm propagation. In this paper, we discuss the global dynamics of SEIQR worm propagation model in mobile internet proposed by Xiao et al. [X. Xiao, P. Fu, C. Dou, Q. Li, G. Hu, and S. Xia, “Design and analysis of SEIQR worm propagation model in mobile internet,” Commun. Nonlinear Sci. Numer. Simulat., vol. 43, pp. 341–350, 2017] to improve and complement the related results. Through a series of mathematical derivations, sufficient conditions are derived to ensure the global exponentially stability of worm-free equilibrium, and the exponential convergent rate can be unveiled. Then, by using the classical geometric approach, it is shown that the endemic equilibrium is globally asymptotically stable and the system is persistent when R 0 > 1. Moreover, numerical simulations are given to demonstrate our theoretical results.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45425622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-18DOI: 10.1515/ijnsns-2021-0073
R. Chaabane, L. Kolsi, A. Jemni, A. D'Orazio
Abstract This study numerically investigates the two-dimensional natural convection in a square enclosure with an isothermal diamond elliptic array at Rayleigh numbers of 104 ≤ Ra ≤ 107. Three cases are considered, i.e., case 1 where two pairs of circular heating bodies are used inside the cavity, one is placed on the vertical centerline (VC) of the cavity and the other on the horizontal centerline (HC), case 2 where one pair of horizontal elliptic heating bodies is placed on the VC of the cavity and the other on the HC and case 3 where the horizontal elliptic heating bodies are replaced by vertical elliptic heating bodies. Numerical simulation was carried out based on the mesoscopic approach (LBM). The effects of the horizontally and vertically heated arrays were investigated. We demonstrate that, only when the Rayleigh number increases to Ra = 107, the numerical solutions reach an unsteady state for all cases. The transition of the flow regime from the unsteady state to the steady state depends on the variation in the ratio of the elliptical cylinder.
{"title":"Buoyancy driven flow characteristics inside a cavity equiped with diamond elliptic array","authors":"R. Chaabane, L. Kolsi, A. Jemni, A. D'Orazio","doi":"10.1515/ijnsns-2021-0073","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0073","url":null,"abstract":"Abstract This study numerically investigates the two-dimensional natural convection in a square enclosure with an isothermal diamond elliptic array at Rayleigh numbers of 104 ≤ Ra ≤ 107. Three cases are considered, i.e., case 1 where two pairs of circular heating bodies are used inside the cavity, one is placed on the vertical centerline (VC) of the cavity and the other on the horizontal centerline (HC), case 2 where one pair of horizontal elliptic heating bodies is placed on the VC of the cavity and the other on the HC and case 3 where the horizontal elliptic heating bodies are replaced by vertical elliptic heating bodies. Numerical simulation was carried out based on the mesoscopic approach (LBM). The effects of the horizontally and vertically heated arrays were investigated. We demonstrate that, only when the Rayleigh number increases to Ra = 107, the numerical solutions reach an unsteady state for all cases. The transition of the flow regime from the unsteady state to the steady state depends on the variation in the ratio of the elliptical cylinder.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44661718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-09DOI: 10.1515/ijnsns-2021-0468
H. Ismael, S. El‐Ganaini, H. Bulut
Abstract In this work, the dynamical behaviors of the Jimbo–Miwa equation that describes certain interesting (3 + 1)-dimensional waves in physics but does not pass any of the conventional integrability tests are studied. One-, two-, and three-M-lump waves are constructed successfully. Interactions between one-M-lump and one-soliton wave, between one-M-lump and two-soliton wave as well as between two-M-lump and one-soliton solution are reported. Also, complex multi-soliton, solutions are offered. The simplified Hirota’s method and a long-wave method are used to construct these types of solutions. The velocity of a one-M-lump wave is studied. Straight Lines of travel for M-lump waves are also reported. To our knowledge, all gained solutions in this research paper are novel and not reported beforehand. Moreover, the gained solutions are presented graphically in three dimensions to better understand the physical phenomena of the suggested equation.
{"title":"M-lump waves and their interactions with multi-soliton solutions for the (3 + 1)-dimensional Jimbo–Miwa equation","authors":"H. Ismael, S. El‐Ganaini, H. Bulut","doi":"10.1515/ijnsns-2021-0468","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0468","url":null,"abstract":"Abstract In this work, the dynamical behaviors of the Jimbo–Miwa equation that describes certain interesting (3 + 1)-dimensional waves in physics but does not pass any of the conventional integrability tests are studied. One-, two-, and three-M-lump waves are constructed successfully. Interactions between one-M-lump and one-soliton wave, between one-M-lump and two-soliton wave as well as between two-M-lump and one-soliton solution are reported. Also, complex multi-soliton, solutions are offered. The simplified Hirota’s method and a long-wave method are used to construct these types of solutions. The velocity of a one-M-lump wave is studied. Straight Lines of travel for M-lump waves are also reported. To our knowledge, all gained solutions in this research paper are novel and not reported beforehand. Moreover, the gained solutions are presented graphically in three dimensions to better understand the physical phenomena of the suggested equation.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48582969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-09DOI: 10.1515/ijnsns-2021-0410
He Yang, Jihong Wang
Abstract The optimal control, for a class of nonlinear neutral evolution equations involving Riemann–Liouville fractional derivative, is investigated in this paper by using Darbo–Sadovskii fixed point theorem. An example is given in the last section to illustrate the validity of the abstract conclusions.
{"title":"Optimal control for a class of fractional order neutral evolution equations","authors":"He Yang, Jihong Wang","doi":"10.1515/ijnsns-2021-0410","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0410","url":null,"abstract":"Abstract The optimal control, for a class of nonlinear neutral evolution equations involving Riemann–Liouville fractional derivative, is investigated in this paper by using Darbo–Sadovskii fixed point theorem. An example is given in the last section to illustrate the validity of the abstract conclusions.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42888175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-08DOI: 10.1515/ijnsns-2021-0423
Mamta Kapoor
Abstract In the present study, time-fractional Schrödinger equations are dealt with for the analytical solution using an integral transform named Shehu Transform. Three kinds of time-fractional Schrödinger equations are discussed in the present study. Shehu transform is utilized to reduce the time-fractional PDE along with the fractional derivative in the Caputo sense. The present method is easy to implement in the search for an analytical solution. As no discretization or numerical program is required, the present scheme will surely be helpful in finding the analytical solution to some complex-natured fractional PDEs.
{"title":"Shehu transform on time-fractional Schrödinger equations – an analytical approach","authors":"Mamta Kapoor","doi":"10.1515/ijnsns-2021-0423","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0423","url":null,"abstract":"Abstract In the present study, time-fractional Schrödinger equations are dealt with for the analytical solution using an integral transform named Shehu Transform. Three kinds of time-fractional Schrödinger equations are discussed in the present study. Shehu transform is utilized to reduce the time-fractional PDE along with the fractional derivative in the Caputo sense. The present method is easy to implement in the search for an analytical solution. As no discretization or numerical program is required, the present scheme will surely be helpful in finding the analytical solution to some complex-natured fractional PDEs.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41438278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-05DOI: 10.1515/ijnsns-2021-0358
Govindaraj Venkatesan, Suresh Kumar Pitchaikkannu
Abstract In this paper, we discuss the trajectory controllability of linear and nonlinear fractional Langevin dynamical systems represented by the Caputo fractional derivative by using the Mittag–Leffler function and Gronwall–Bellman inequality. For the nonlinear system, we assume Lipschitz-type conditions on the nonlinearity. Examples are given to illustrate the theoretical results.
{"title":"Trajectory controllability of nonlinear fractional Langevin systems","authors":"Govindaraj Venkatesan, Suresh Kumar Pitchaikkannu","doi":"10.1515/ijnsns-2021-0358","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0358","url":null,"abstract":"Abstract In this paper, we discuss the trajectory controllability of linear and nonlinear fractional Langevin dynamical systems represented by the Caputo fractional derivative by using the Mittag–Leffler function and Gronwall–Bellman inequality. For the nonlinear system, we assume Lipschitz-type conditions on the nonlinearity. Examples are given to illustrate the theoretical results.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46247133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-03DOI: 10.1515/ijnsns-2021-0321
K. Anukiruthika, N. Durga, P. Muthukumar
Abstract The optimal control of non-instantaneous impulsive second-order stochastic McKean–Vlasov evolution system with Clarke subdifferential and mixed fractional Brownian motion is investigated in this article. The deterministic nonlinear second-order controlled partial differential system is enriched with stochastic perturbations, non-instantaneous impulses, and Clarke subdifferential. In particular, the nonlinearities in the system that rely on the state of the solution are allowed to rely on the corresponding probability distribution of the state. The solvability of the considered system is discussed with the help of stochastic analysis, multivalued analysis, and multivalued fixed point theorem. Further, the existence of optimal control is established with the aid of Balder’s theorem. Finally, an example is provided to illustrate the developed theory.
{"title":"Optimal control of non-instantaneous impulsive second-order stochastic McKean–Vlasov evolution system with Clarke subdifferential","authors":"K. Anukiruthika, N. Durga, P. Muthukumar","doi":"10.1515/ijnsns-2021-0321","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0321","url":null,"abstract":"Abstract The optimal control of non-instantaneous impulsive second-order stochastic McKean–Vlasov evolution system with Clarke subdifferential and mixed fractional Brownian motion is investigated in this article. The deterministic nonlinear second-order controlled partial differential system is enriched with stochastic perturbations, non-instantaneous impulses, and Clarke subdifferential. In particular, the nonlinearities in the system that rely on the state of the solution are allowed to rely on the corresponding probability distribution of the state. The solvability of the considered system is discussed with the help of stochastic analysis, multivalued analysis, and multivalued fixed point theorem. Further, the existence of optimal control is established with the aid of Balder’s theorem. Finally, an example is provided to illustrate the developed theory.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46345654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-11DOI: 10.1515/ijnsns-2021-0244
Varunkumar Merugu, Muthu Poosan
Abstract In this paper, a mathematical model for the steady laminar, incompressible and Newtonian fluid flow in a proximal renal tubule is presented. In this, the tubule is considered as a tapered tube with double constriction and permeable boundary. The impact of the fluid reabsorption across the tubule wall is assumed as the occurrence of exponentially decreasing flow at each cross-section. The present model is formulated through the Navier–Stokes equations, under the appropriate boundary conditions. A regular perturbation technique is used to obtain the approximate solutions. This study brings out the significant impacts of reabsorption coefficient (α) and tapered angle (ϕ) on the flow variables such as velocities, the drop in pressure, and wall shear stress are discussed through graphs. The streamlines are also plotted to understand the influence of the reabsorption and tapering phenomena on the flow.
{"title":"Mathematical model of fluid flow in a double constricted tapered tube with permeable boundary","authors":"Varunkumar Merugu, Muthu Poosan","doi":"10.1515/ijnsns-2021-0244","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0244","url":null,"abstract":"Abstract In this paper, a mathematical model for the steady laminar, incompressible and Newtonian fluid flow in a proximal renal tubule is presented. In this, the tubule is considered as a tapered tube with double constriction and permeable boundary. The impact of the fluid reabsorption across the tubule wall is assumed as the occurrence of exponentially decreasing flow at each cross-section. The present model is formulated through the Navier–Stokes equations, under the appropriate boundary conditions. A regular perturbation technique is used to obtain the approximate solutions. This study brings out the significant impacts of reabsorption coefficient (α) and tapered angle (ϕ) on the flow variables such as velocities, the drop in pressure, and wall shear stress are discussed through graphs. The streamlines are also plotted to understand the influence of the reabsorption and tapering phenomena on the flow.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41398586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-08DOI: 10.1515/ijnsns-2021-0278
Pushpendra Kumar, V. S. Erturk, M. Murillo‐Arcila, C. Harley
Abstract In this article, we propose generalized forms of three well-known fractional numerical methods namely Euler, Runge–Kutta 2-step, and Runge–Kutta 4-step, respectively. The new versions we provide of these methods are derived by utilizing a non-uniform grid which is slightly different from previous versions of these algorithms. A new generalized form of the well-known Caputo-type fractional derivative is used to derive the results. All necessary analyses related to the stability, convergence, and error bounds are also provided. The precision of all simulated results is justified by performing multiple numerical experiments, with some meaningful problems solved by implementing the code in Mathematica. Finally, we give a brief discussion on the simulated results which shows that the generalized methods are novel, effective, reliable, and very easy to implement.
{"title":"Generalized forms of fractional Euler and Runge–Kutta methods using non-uniform grid","authors":"Pushpendra Kumar, V. S. Erturk, M. Murillo‐Arcila, C. Harley","doi":"10.1515/ijnsns-2021-0278","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0278","url":null,"abstract":"Abstract In this article, we propose generalized forms of three well-known fractional numerical methods namely Euler, Runge–Kutta 2-step, and Runge–Kutta 4-step, respectively. The new versions we provide of these methods are derived by utilizing a non-uniform grid which is slightly different from previous versions of these algorithms. A new generalized form of the well-known Caputo-type fractional derivative is used to derive the results. All necessary analyses related to the stability, convergence, and error bounds are also provided. The precision of all simulated results is justified by performing multiple numerical experiments, with some meaningful problems solved by implementing the code in Mathematica. Finally, we give a brief discussion on the simulated results which shows that the generalized methods are novel, effective, reliable, and very easy to implement.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48381884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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