International Journal of Computer Mathematics最新文献

{"title":"The Robust Numerical Schemes for Two-Dimensional Elliptical Singularly Perturbed Problems with Space Shifts","authors":"None Garima, Kapil K Sharma","doi":"10.1080/00207160.2023.2269438","DOIUrl":"https://doi.org/10.1080/00207160.2023.2269438","url":null,"abstract":"AbstractThis article focuses on the investigation of two-dimensional elliptic singularly perturbed problems that incorporate positive and negative shifts, the solution of this class of problems may demonstrate regular/parabolic/degenerate or interior boundary layers. The goal of this article is to establish the development of numerical techniques for two-dimensional elliptic singularly perturbed problems with positive and negative shifts having regular boundary layers. The three numerical schemes are proposed to estimate the solution of this class of problems based on the fitted operator and fitted mesh finite-difference methods. The fitted operator finite difference method is analyzed for convergence. The effect of shift terms on the solution behavior is demonstrated through numerical experiments. The paper concludes by providing several numerical results that demonstrate the performance of these three numerical schemes.Keywords: Singularly perturbed problemDifferential-difference equationsUpwind SchemeHybrid SchemeFitted operator finite-difference methodDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThe first author acknowledges the financial support received from the Council of Scientific and Industrial Research (File No.- 09/1112(0006)/2018-EMR-I) in the form of Senior Research Fellowship.Conflict of interestThe authors declare that they have no conflict of interest.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136293741","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}

{"title":"A block-by-block approach for nonlinear fractional integro-differential equations","authors":"F. Afiatdoust, M. H. Heydari, M. M. Hosseini","doi":"10.1080/00207160.2023.2265500","DOIUrl":"https://doi.org/10.1080/00207160.2023.2265500","url":null,"abstract":"AbstractIn this paper, a block-by-block scheme is proposed for a class of nonlinear fractional integro-differential equations. This method is based on the Gauss-Lobatto numerical integration method, which shows the high accuracy at all time intervals. Also, the method convergence for this type of equations is proved and it is shown that the order of convergence is at least eight. Finally, the high accuracy, fast calculations and good performance of the method are investigated by solving some numerical examples.Keywords: Nonlinear fractional integro-differentia equationsGauss-Lobatto quadrature ruleBlock-by-block methodDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134946922","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}

{"title":"Efficient Pricing and Calibration of High-Dimensional Basket Options","authors":"Lech A. Grzelak, Juliusz Jablecki, Dariusz Gatarek","doi":"10.1080/00207160.2023.2266051","DOIUrl":"https://doi.org/10.1080/00207160.2023.2266051","url":null,"abstract":"AbstractThis paper studies equity basket options – i.e. multi-dimensional derivatives whose payoffs depend on the value of a weighted sum of the underlying stocks – and develops a new and innovative approach to ensure consistency between options on individual stocks and on the index comprising them. Specifically, we show how to resolve a well-known problem that when individual constituent distributions of an equity index are inferred from the single-stock option markets and combined in a multi-dimensional local/stochastic volatility model, the resulting basket option prices will not generate a skew matching that of the options on the equity index corresponding to the basket. To address this “insufficient skewness”, we proceed in two steps. First, we propose an “effective” local volatility model by mapping the general multi-dimensional basket onto a collection of marginal distributions. Second, we build a multivariate dependence structure between all the marginal distributions assuming a jump-diffusion model for the effective projection parameters, and show how to calibrate the basket to the index smile. Numerical tests and calibration exercises demonstrate an excellent fit for a basket of as many as 30 stocks with fast calculation time.Keywords: Basket OptionsIndex SkewMonte CarloLocal VolatilityStochastic VolatilityCollocation MethodsDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. Notes1 Cf. the prospectus availible in the online records of the U.S. Securities and Exchange Commission at: https://www.sec.gov/Archives/edgar/data/19617/000089109221003578/e13291-424b2.htm2 For example, in the Bloomberg basket options pricing template correlations are, by default, estimated over a 5 year period, whereby to eliminate noise, a given percentile of rolling 6-month cross-correlation estimates is chosen in the parameterization of the full correlation matrix.3 We define the skew here loosely as the difference in implied volatilities between the 85-120% ATM levels.4 As an alternative to [27] one could consider Kou's jump-diffusion model [18] which has the additional benefit of separating the upside and downside skew. However, in this case, we opt for the simplicity and parsimony of Merton's approach5 Without loss of generality, we shall henceforth think of the underlying assets as stocks, however the method developed below is obviously general and, mutatis mutandis, applies to other instruments as well.6 The proposed framework can also be extended with a stochastic volatility process. Such an extension is trivial and will, for simplicity, be omitted.7 The respective dynami","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135696060","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}

{"title":"A two-grid virtual element method for nonlinear variable-order time-fractional diffusion equation on polygonal meshes","authors":"Qiling Gu, Yanping Chen, Jianwei Zhou, Yunqing Huang","doi":"10.1080/00207160.2023.2263589","DOIUrl":"https://doi.org/10.1080/00207160.2023.2263589","url":null,"abstract":"AbstractIn this paper, we develop a two-grid virtual element method for nonlinear variable-order time-fractional diffusion equation on polygonal meshes. The L1 graded mesh scheme is considered in the time direction, and the VEM is used to approximate spatial direction. The two-grid virtual element algorithm reduces the solution of the nonlinear time fractional problem on a fine grid to one linear equation on the same fine grid and an original nonlinear problem on a much coarser grid. As a result, our algorithm not only saves total computational cost, but also maintains the optimal accuracy. Optimal L2 error estimates are analysed in detail for both the VEM scheme and the corresponding two-grid VEM scheme. Finally, numerical experiments presented confirm the theoretical findings.Keywords: Virtual element methodnonlinearvariable-order fractional equationtwo-gridpolygonal meshesa priori error estimateMathematics subject classifications: 65M6065N3034K3765M1565M55 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work is supported by the State Key Program of National Natural Science Foundation of China [grant number 11931003] and National Natural Science Foundation of China [grant number 41974133], Hunan Provincial Innovation Foundation for Postgraduate, China [grant number XDCX2021B098], Postgraduate Scientific Research Innovation Project of Hunan Province [grant number CX20210597].","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135744159","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}

{"title":"Truncated Euler–Maruyama method for stochastic differential equations driven by fractional Brownian motion with super-linear drift coefficient","authors":"Jie He, Shuaibin Gao, Weijun Zhan, Qian Guo","doi":"10.1080/00207160.2023.2266757","DOIUrl":"https://doi.org/10.1080/00207160.2023.2266757","url":null,"abstract":"AbstractIn this paper, we propose a truncated Euler-Maruyama scheme for stochastic differential equations driven by fractional Brownian motion with super-linear drift coefficient. Meanwhile, the convergence rate of the numerical method is established. Numerical example is demonstrated to verify the theoretical results.Keywords: Truncated Euler–Maruyamastochastic differential equationfractional Brownian motionconvergence rateDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThis work was supported by the National Natural Science Foundation of China (11871343).5. References","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135739674","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}

{"title":"Effective numerical computation of p(x)-Laplace equations in 2D","authors":"Adriana Aragón, Julián Fernández Bonder, Diana Rubio","doi":"10.1080/00207160.2023.2263103","DOIUrl":"https://doi.org/10.1080/00207160.2023.2263103","url":null,"abstract":"In this article we implement a method for the computation of a nonlinear elliptic problem with nonstandard growth driven by the Laplacian operator. Our implementation is based in the decomposition–coordination method that allows us, via an iterative process, to solve in each step a linear differential equation and a nonlinear algebraic equation. Our code is implemented in MatLab in two dimensions and turns out to be extremely efficient from the computational point of view.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135323624","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}

{"title":"Linear and Nonlinear Dirichlet-Neumann Method in Multiple Subdomains for the Cahn-Hilliard Equation","authors":"Gobinda Garai, Bankim C. Mandal","doi":"10.1080/00207160.2023.2266068","DOIUrl":"https://doi.org/10.1080/00207160.2023.2266068","url":null,"abstract":"AbstractIn this paper, we propose and present a non-overlapping substructuring type iterative algorithm for the Cahn-Hilliard (CH) equation, which is a prototype for phase-field models. It is of great importance to develop efficient numerical methods for the CH equation, given the range of applicability of CH equation has. Here we present a formulation for the linear and non-linear Dirichlet-Neumann (DN) method applied to the CH equation and study the convergence behaviour in one and two spatial dimension in multiple subdomains. We show numerical experiments to illustrate our theoretical findings and effectiveness of the method.Keywords: Dirichlet-NeumannCahn-Hilliard equationParallel computingDomain decompositionConvergence analysisAMS subject classifications: 65M5565Y0565M15DisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThe authors would like to thank the CSIR India (File No:09/1059(0019)/2018-EMR-I) and DST-SERB (File No: SRG/2019/002164) for the financial assistance and IIT Bhubaneswar for research facility.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135247591","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}

{"title":"General Solution of Two-dimensional Singular Fractional Linear Continuous-Time System Using the conformable derivative and Sumudu transform","authors":"Kamel Benyettou, Djillali Bouagada, Mohammed Amine Ghezzar","doi":"10.1080/00207160.2023.2262056","DOIUrl":"https://doi.org/10.1080/00207160.2023.2262056","url":null,"abstract":"AbstractThe effectiveness of this paper lies in presenting a new solution for the singular fractional two dimensional linear continuous-time systems using the conformable derivative and Sumudu transform. The proposed technique combines the new advantageous features of conformal derivative and double-delta-Kronecker, which efficiently handles singularities and Sumudu transform, and provides an efficient solution for 2D singular Fornasini-Marchesini fractional models. Applying these approaches, we then derive new explicit expressions for the fundamental matrices of the considered model. The applicability and usefulness of our proposed methods are validated and evaluated by numerical simulations in order to show the accuracy of the obtained results.Keywords: Fractional linear systemsConformable derivativeDouble Laplace transformDouble Sumudu transformFornasini-Marchesini modelsFundamental matrixSingular systemsDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThis paper presents research results of the ACSY-Team (Analysis & Control systems team) and of the doctorial training on the Operational Research from the Pure and Applied mathematics Laboratory UMAB and Decision Support funded by the General Directorate for Scientific Research and Technological Development of Algeria (DGRSDT) and supported by National Higher School of Mathematics (NHSM), University of Mostaganem Abdelhamid Ibn Badis (UMAB) and initiated by the concerted research project on Control and Systems theory (PRFU Project Code C00L03UN270120200003).","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135343614","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}

{"title":"Numerical solution of nonlinear third kind Volterra integral equations using an iterative collocation method","authors":"Khedidja Kherchouche, Azzeddine Bellour, Pedro Lima","doi":"10.1080/00207160.2023.2260007","DOIUrl":"https://doi.org/10.1080/00207160.2023.2260007","url":null,"abstract":"AbstractIn this paper, we discuss the application of an iterative collocation method based on the use of Lagrange polynomials for the numerical solution of a class of nonlinear third kind Volterra integral equations. The approximate solution is given by explicit formulas. The error analysis of the proposed numerical method is studied theoretically. Some numerical examples are given to confirm our theoretical results.Keywords: Nonlinear third kind Volterra integral equationCollocation methodIterative methodLagrange polynomialsConvergence analysis.DisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThe third author (P. Lima) acknowledges financial support from FCT, through projects UIDB/04621/2020, UIDP/04621/2020.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135768938","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}

{"title":"On the simultaneous reconstruction of the initial diffusion time and source term for the time-fractional diffusion equation","authors":"Zhousheng Ruana, Zhenxing Chena, Min Luoa, Wen Zhang","doi":"10.1080/00207160.2023.2260011","DOIUrl":"https://doi.org/10.1080/00207160.2023.2260011","url":null,"abstract":"AbstractFacing application in real world, a simultaneous identification problem of determining the initial diffusion time (or the length of diffusion time) and source term in a time fractional diffusion equation is investigated. First the simultaneous reconstruction problem is proposed by translating the Caputo fractional derivative. Then the uniqueness results for the simultaneous identification problem are proven by the technique of analytic continuation and the Laplace transformation method. Next the Lipschitz continuousness of the observation operator is derived, and an alternating direction inversion algorithm is proposed to solve the simultaneous identification problem. At last, several numerical examples are computed to show the efficiency and stability of the reconstruction algorithm.Keywords: Simultaneous identificationthe length of diffusion timeinverse source problemuniquenesstime-fractional diffusion equation2000 MR Subject Classification: 65M0665M1265M32DisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThis work is supported by National Natural Science Foundation of China (12061008, 11861007, 11961002), Natural Science Foundation of Jiangxi Province of China (20202BABL 201004).","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136129480","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}