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Numerical solution of general Emden–Fowler equation using Haar wavelet collocation method 用Haar小波配点法数值解一般Emden-Fowler方程
IF 1.8 4区 数学
International Journal of Computer Mathematics Pub Date : 2023-07-21 DOI: 10.1080/00207160.2023.2239948
Ashisha Kumar, P. Goswami
{"title":"Numerical solution of general Emden–Fowler equation using Haar wavelet collocation method","authors":"Ashisha Kumar, P. Goswami","doi":"10.1080/00207160.2023.2239948","DOIUrl":"https://doi.org/10.1080/00207160.2023.2239948","url":null,"abstract":"This paper deals with the numerical solution of the general Emden–Fowler equation using the Haar wavelet collocation method. This method transforms the differential equation into a system of nonlinear equations. These equations are further solved by Newton's method to obtain the Haar coefficients, and finally the solution to the problem is acquired using these coefficients. We have taken many examples of fifth- and sixth-order equations and implemented our method on those examples. The graphs show the efficiency of the solution for resolution L = 3 and the maximum absolute error of our approach. The error tables give a good picture of the accuracy of this approach.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77203312","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}
引用次数: 0
A study on mild solutions for multi-term time fractional measure differential equations 多项时间分数测度微分方程温和解的研究
IF 1.8 4区 数学
International Journal of Computer Mathematics Pub Date : 2023-07-21 DOI: 10.1080/00207160.2023.2239943
Haide Gou, Y. Jia
{"title":"A study on mild solutions for multi-term time fractional measure differential equations","authors":"Haide Gou, Y. Jia","doi":"10.1080/00207160.2023.2239943","DOIUrl":"https://doi.org/10.1080/00207160.2023.2239943","url":null,"abstract":"In this paper, we investigate the existence and uniqueness of the S-asymptotically ω-periodic mild solutions to a class of multi-term time-fractional measure differential equations with initial conditions in Banach spaces. Firstly, we look for a suitable concept of S-asymptotically ω-periodic mild solution to our concerned problem, by means of the Laplace transform and -resolvent family . Secondly, the existence of S-asymptotically ω-periodic mild solutions for the mentioned system is obtained by utilizing regulated functions and fixed point theorem. Finally, as the application of abstract results, an example is given to illustrate our main results.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89976289","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}
引用次数: 0
A new high-accuracy difference method for nonhomogeneous time-fractional Schrödinger equation 非齐次时间分数阶Schrödinger方程的高精度差分新方法
IF 1.8 4区 数学
International Journal of Computer Mathematics Pub Date : 2023-06-30 DOI: 10.1080/00207160.2023.2226254
Zihao Tian, Yanhua Cao, Xiaozhong Yang
{"title":"A new high-accuracy difference method for nonhomogeneous time-fractional Schrödinger equation","authors":"Zihao Tian, Yanhua Cao, Xiaozhong Yang","doi":"10.1080/00207160.2023.2226254","DOIUrl":"https://doi.org/10.1080/00207160.2023.2226254","url":null,"abstract":"The fractional Schrödinger equation is an important fractional nonlinear evolution equation, and the study of its numerical solution has profound scientific meaning and wide application prospects. This paper proposes a new high-accuracy difference method for nonhomogeneous time-fractional Schrödinger equation (TFSE). The Caputo time-fractional derivative is discretized by high-order formula and the fourth-order compact difference approximation is applied for spatial discretization. A new nonlinear compact difference scheme with temporal second-order and spatial fourth-order accuracy is constructed, which is solved by the efficient linearized iterative algorithm. The unconditional stability and convergence are analysed by the energy method. The unique existence and maximum-norm estimate of new compact difference scheme solution are obtained. Theoretical analysis shows that the convergence accuracy of new compact difference scheme is with the strong regularity assumption. Numerical experiments verify theoretical results and indicate that the proposed method is an efficient numerical method for solving TFSE.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77696109","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}
引用次数: 0
On the numerical solution of a population growth model of a species living in a closed system based on the moving least squares scheme 基于移动最小二乘格式的封闭系统物种种群增长模型的数值解
IF 1.8 4区 数学
International Journal of Computer Mathematics Pub Date : 2023-06-19 DOI: 10.1080/00207160.2023.2214254
F. Asadi-Mehregan, P. Assari, M. Dehghan
{"title":"On the numerical solution of a population growth model of a species living in a closed system based on the moving least squares scheme","authors":"F. Asadi-Mehregan, P. Assari, M. Dehghan","doi":"10.1080/00207160.2023.2214254","DOIUrl":"https://doi.org/10.1080/00207160.2023.2214254","url":null,"abstract":"In this research paper, we introduce a numerical approach to solve a particular type of nonlinear integro-differential equations derived from Volterra's population model. This model characterizes the growth of a biological species in a closed system and includes an integral term to consider the influence of toxin accumulation on the species, along with the conventional terms found in the logistic equation. The proposed technique estimates the solution of integro-differential equations utilizing the discrete Galerkin scheme using the moving least squares (MLS) algorithm. The locally weighted least squares polynomial fitting, known as the MLS method, is a valuable approach for approximating unknown functions. Since the offered scheme does not require any cell structures, it can be known as a meshless local discrete Galerkin method. Moreover, we obtain the error estimate of the proposed approach. The validity and efficiency of the newly developed technique are assessed over several nonlinear integro-differential equations.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79123669","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}
引用次数: 0
A mollification regularization method with Dirichlet kernel to solve potential-free field inverse Schrödinger Cauchy problem 求解无势场逆Schrödinger柯西问题的狄利克雷核软化正则化方法
IF 1.8 4区 数学
International Journal of Computer Mathematics Pub Date : 2023-06-10 DOI: 10.1080/00207160.2023.2217716
Lan Yang, Lin Zhu, Shangqin He
{"title":"A mollification regularization method with Dirichlet kernel to solve potential-free field inverse Schrödinger Cauchy problem","authors":"Lan Yang, Lin Zhu, Shangqin He","doi":"10.1080/00207160.2023.2217716","DOIUrl":"https://doi.org/10.1080/00207160.2023.2217716","url":null,"abstract":"","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78363210","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}
引用次数: 0
Convergence analysis of a novel fractional product integration method for solving the second kind weakly singular Volterra integral equations with non-smooth solutions based on Jacobi polynomials 基于Jacobi多项式求解第二类弱奇异Volterra非光滑积分方程的分数阶积积分新方法的收敛性分析
IF 1.8 4区 数学
International Journal of Computer Mathematics Pub Date : 2023-06-01 DOI: 10.1080/00207160.2023.2214643
Sayed Arsalan Sajjadi, H. Najafi, H. Aminikhah
{"title":"Convergence analysis of a novel fractional product integration method for solving the second kind weakly singular Volterra integral equations with non-smooth solutions based on Jacobi polynomials","authors":"Sayed Arsalan Sajjadi, H. Najafi, H. Aminikhah","doi":"10.1080/00207160.2023.2214643","DOIUrl":"https://doi.org/10.1080/00207160.2023.2214643","url":null,"abstract":"In this paper, we introduce a new fractional basis function based on Lagrange polynomials. We define the new interpolation formula for approximation of the solutions of the second kind weakly singular Volterra integral equations. The product integration method is used for the numerical solution of these equations based on Jacobi polynomials. It is known that the weakly singular Volterra integral equations typically have solutions whose derivatives are unbounded at the left end-point of the interval of integration. We use the suitable transformations to overcome this non-smooth behaviour. An upper error bound of the proposed method is determined and the convergence analysis is discussed. Finally, some numerical examples with non-smooth solutions are prepared to test the efficiency and accuracy of the method.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86464010","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}
引用次数: 0
Approximating solutions of the generalized modification of the system of equilibrium problems and fixed point problem of a nonexpansive mapping 非膨胀映射的平衡问题和不动点问题系统的广义修正的逼近解
IF 1.8 4区 数学
International Journal of Computer Mathematics Pub Date : 2023-05-27 DOI: 10.1080/00207160.2023.2217303
Kanyanee Saechou, A. Kangtunyakarn
{"title":"Approximating solutions of the generalized modification of the system of equilibrium problems and fixed point problem of a nonexpansive mapping","authors":"Kanyanee Saechou, A. Kangtunyakarn","doi":"10.1080/00207160.2023.2217303","DOIUrl":"https://doi.org/10.1080/00207160.2023.2217303","url":null,"abstract":"The purpose of this research is to study the generalized modification of the system of equilibrium problems (GMSEP) and a lemma is established to show the property of this problem. Then, we prove a strong convergence theorem for finding a common element of the set of the solutions of the fixed points problem and the set of the solutions of the GMSEP under some suitable conditions, in which , where are coefficients in the main iteration. Moreover, we prove strong convergence theorems for finding solutions to the generalized equilibrium problem, the system of equilibrium problems, the variational inequality problem, the general system of variational inequality problems, and the minimization problem. Finally, we give two numerical examples, one of which shows the rate of convergence of the main iteration while the other shows the rate of convergence of the main iteration but the sum of coefficients equals 1.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88731623","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}
引用次数: 0
Higher-order breather, lump and hybrid solutions of (2 + 1)-dimensional coupled nonlinear evolution equations with time-dependent coefficients 具有时变系数的(2 + 1)维耦合非线性演化方程的高阶呼吸、整体和混合解
IF 1.8 4区 数学
International Journal of Computer Mathematics Pub Date : 2023-05-26 DOI: 10.1080/00207160.2023.2219349
Chen J. Wang, Houping Dai, Meng-jun Li, Yinghua Feng
{"title":"Higher-order breather, lump and hybrid solutions of (2 + 1)-dimensional coupled nonlinear evolution equations with time-dependent coefficients","authors":"Chen J. Wang, Houping Dai, Meng-jun Li, Yinghua Feng","doi":"10.1080/00207160.2023.2219349","DOIUrl":"https://doi.org/10.1080/00207160.2023.2219349","url":null,"abstract":"This paper investigates a class of (2 + 1)-dimensional coupled nonlinear evolution equation with time-dependent coefficients in an inhomogeneous medium via the Hirota bilinear method. Combining the long wave limit method and complex conjugate transform, the higher-order breather and lump solutions are initially constructed. Furthermore, hybrid solutions among N-soliton, lump and breather solutions are derived by linear constraints on the parameters. Meanwhile, the dynamic evolution behaviour of some special concrete solutions under different time-dependent coefficients is presented visually in the form of images.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81464449","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}
引用次数: 0
Generalized multistep Steffensen iterative method. Solving the model of a photomultiplier device 广义多步Steffensen迭代法。求解光电倍增管器件的模型
IF 1.8 4区 数学
International Journal of Computer Mathematics Pub Date : 2023-05-25 DOI: 10.1080/00207160.2023.2217307
Eva G. Villalba, J. L. Hueso, E. Martínez
{"title":"Generalized multistep Steffensen iterative method. Solving the model of a photomultiplier device","authors":"Eva G. Villalba, J. L. Hueso, E. Martínez","doi":"10.1080/00207160.2023.2217307","DOIUrl":"https://doi.org/10.1080/00207160.2023.2217307","url":null,"abstract":"It is well known that the Steffensen-type methods approximate the derivative appearing in Newton's scheme by means of the first-order divided difference operator. The generalized multistep Steffensen iterative method consists of composing the method with itself m times. Specifically, the divided difference is held constant for every m steps before it is updated. In this work, we introduce a modification to this method, in order to accelerate the convergence order. In the proposed, scheme we compute the divided differences in first and second step and use the divided difference from the second step in the following m−1 steps. We perform an exhaustive study of the computational efficiency of this scheme and also introduce memory to this method to speed up convergence without performing new functional evaluations. Finally, some numerical examples are studied to verify the usefulness of these algorithms.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81272053","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}
引用次数: 0
A new options pricing method: semi-stochastic kernel regression method with constraints 一种新的期权定价方法:带约束的半随机核回归法
IF 1.8 4区 数学
International Journal of Computer Mathematics Pub Date : 2023-05-22 DOI: 10.1080/00207160.2023.2217302
Le Jiang, Cheng-long Xu
{"title":"A new options pricing method: semi-stochastic kernel regression method with constraints","authors":"Le Jiang, Cheng-long Xu","doi":"10.1080/00207160.2023.2217302","DOIUrl":"https://doi.org/10.1080/00207160.2023.2217302","url":null,"abstract":"This paper presents a unified semi-stochastic kernel regression method for pricing options under general stochastic volatility model. The method combines semi-stochastic sampling for initial asset values with Monte Carlo simulations to construct a least-squares based kernel function regression solution. This approach can not only approximates option prices, but also determines the Greeks of option. The least square problem is augmented with weighted derivative constraints, which enables flexible adjustment of approximate errors for both option prices and Greeks. Numerical results show the efficiency of the proposed method for the Vanilla option and some exotic options: Asian option, Lookback option, discretely monitored Barrier option and the Basket option with several assets under the stochastic volatility model.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78614667","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}
引用次数: 0
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