Pub Date : 2025-12-13DOI: 10.1016/j.cam.2025.117253
Wenxuan Zhang , Yixiao Guo , Benzhuo Lu
This paper proposes the Exact Terminal Condition Neural Network (ETCNN), a deep learning framework for accurately pricing American options by solving the Black–Scholes–Merton (BSM) equations. The ETCNN incorporates carefully designed functions that ensure the numerical solution not only exactly satisfies the terminal condition of the BSM equations but also matches the non-smooth and singular behavior of the option price near expiration. This method effectively addresses the challenges posed by the inequality constraints in the BSM equations and can be easily extended to high-dimensional scenarios. Additionally, input normalization is employed to maintain the homogeneity. Multiple experiments are conducted to demonstrate that the proposed method achieves high accuracy and exhibits robustness across various situations, outperforming both traditional numerical methods and other machine learning approaches.
{"title":"Exact terminal condition neural network for American option pricing based on the Black–Scholes–Merton equations","authors":"Wenxuan Zhang , Yixiao Guo , Benzhuo Lu","doi":"10.1016/j.cam.2025.117253","DOIUrl":"10.1016/j.cam.2025.117253","url":null,"abstract":"<div><div>This paper proposes the Exact Terminal Condition Neural Network (ETCNN), a deep learning framework for accurately pricing American options by solving the Black–Scholes–Merton (BSM) equations. The ETCNN incorporates carefully designed functions that ensure the numerical solution not only exactly satisfies the terminal condition of the BSM equations but also matches the non-smooth and singular behavior of the option price near expiration. This method effectively addresses the challenges posed by the inequality constraints in the BSM equations and can be easily extended to high-dimensional scenarios. Additionally, input normalization is employed to maintain the homogeneity. Multiple experiments are conducted to demonstrate that the proposed method achieves high accuracy and exhibits robustness across various situations, outperforming both traditional numerical methods and other machine learning approaches.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"480 ","pages":"Article 117253"},"PeriodicalIF":2.6,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-11DOI: 10.1016/j.cam.2025.117247
Dimitri Breda , Dajana Conte , Raffaele D’Ambrosio , Ida Santaniello , Muhammad Tanveer
A general framework for recovering drift and diffusion dynamics from sampled trajectories is presented for the first time for stochastic delay differential equations. The core relies on the well-established SINDy algorithm for the sparse identification of nonlinear dynamics. The proposed methodology combines recently proposed high-order estimates of drift and covariance for dealing with stochastic problems with augmented libraries to handle delayed arguments. Three different strategies are discussed in view of exploiting only realistically available data. A thorough comparative numerical investigation is performed on different models, which helps guiding the choice of effective and possibly outperforming schemes.
{"title":"Sparse identification of nonlinear dynamics for stochastic delay differential equations","authors":"Dimitri Breda , Dajana Conte , Raffaele D’Ambrosio , Ida Santaniello , Muhammad Tanveer","doi":"10.1016/j.cam.2025.117247","DOIUrl":"10.1016/j.cam.2025.117247","url":null,"abstract":"<div><div>A general framework for recovering drift and diffusion dynamics from sampled trajectories is presented for the first time for stochastic delay differential equations. The core relies on the well-established SINDy algorithm for the sparse identification of nonlinear dynamics. The proposed methodology combines recently proposed high-order estimates of drift and covariance for dealing with stochastic problems with augmented libraries to handle delayed arguments. Three different strategies are discussed in view of exploiting only realistically available data. A thorough comparative numerical investigation is performed on different models, which helps guiding the choice of effective and possibly outperforming schemes.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"479 ","pages":"Article 117247"},"PeriodicalIF":2.6,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-11DOI: 10.1016/j.cam.2025.117251
Nana Adjoah Mbroh , Sergei Stepanov , Maria Vasilyeva , Alexey Sadovski , Hyangim Ji
We consider a time-fractional multispecies competition model in a heterogeneous domain. The mathematical model is described by a coupled system of nonlinear reaction-diffusion equations with a fractional time derivative. Due to the presence of multiple scales in the heterogeneous domain and the memory effect represented in time-fractional partial differential equations, traditional numerical methods would necessitate substantial computational resources to resolve the scale and store previous solutions with a fine-grid resolution. We present a computationally efficient numerical scheme to solve reaction-diffusion equations with a Caputo fractional time derivative. The time discretization is performed using the semi-implicit scheme, and the spatial discretization is based on the finite element method on a fine grid. To construct memory-efficient coarse grid approximation by space, we use a Generalized Multiscale Finite Element Method. We present a construction of two types of multiscale basis functions: offline and online. Offline multiscale space is based on the solution of the local spectral problem and addresses a heterogeneous diffusion coefficient to give a sufficiently accurate coarse grid approximation. On the online stage, we enrich a precomputed offline multiscale space with online residual-based multiscale basis functions. The stability of the time discretization and the convergence of the multiscale scheme are established. A numerical study with varying numbers of basis functions and fractional order α has been presented.
{"title":"Multiscale scheme for a time-fractional multispecies reaction-diffusion model","authors":"Nana Adjoah Mbroh , Sergei Stepanov , Maria Vasilyeva , Alexey Sadovski , Hyangim Ji","doi":"10.1016/j.cam.2025.117251","DOIUrl":"10.1016/j.cam.2025.117251","url":null,"abstract":"<div><div>We consider a time-fractional multispecies competition model in a heterogeneous domain. The mathematical model is described by a coupled system of nonlinear reaction-diffusion equations with a fractional time derivative. Due to the presence of multiple scales in the heterogeneous domain and the memory effect represented in time-fractional partial differential equations, traditional numerical methods would necessitate substantial computational resources to resolve the scale and store previous solutions with a fine-grid resolution. We present a computationally efficient numerical scheme to solve reaction-diffusion equations with a Caputo fractional time derivative. The time discretization is performed using the semi-implicit scheme, and the spatial discretization is based on the finite element method on a fine grid. To construct memory-efficient coarse grid approximation by space, we use a Generalized Multiscale Finite Element Method. We present a construction of two types of multiscale basis functions: offline and online. Offline multiscale space is based on the solution of the local spectral problem and addresses a heterogeneous diffusion coefficient to give a sufficiently accurate coarse grid approximation. On the online stage, we enrich a precomputed offline multiscale space with online residual-based multiscale basis functions. The stability of the time discretization and the convergence of the multiscale scheme are established. A numerical study with varying numbers of basis functions and fractional order <em>α</em> has been presented.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"479 ","pages":"Article 117251"},"PeriodicalIF":2.6,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-11DOI: 10.1016/j.cam.2025.117249
Meltem Evrenosoğlu Adıyaman , Mustafa Kemal Altınbaş , Gülter Budakçı
In this study, a novel approach is proposed to approximate the solution of second order Fredholm integro-differential equations. The proposed method extends the residual method used for solving ordinary differential equations. This method is based on approximating the solution of initial value problems using a Bézier curve. For the extension of the method, some novel formulas are derived to obtain the integral of the product of Bernstein basis functions and analytic functions. The proposed method is also applied to boundary value problems with minor modifications. The most significant feature of the proposed method is its ease of application to various problems, due to its simplicity and flexibility. Error analysis is provided for both initial and boundary value problems, demonstrating that this method achieves a high order of accuracy. In order to demonstrate the accuracy and efficiency of the method, several numerical examples are provided, and their results are compared with those obtained by other methods in the literature. The findings indicate that the proposed method is highly effective and can serve as a viable alternative to existing techniques for solving Fredholm integro-differential equations.
{"title":"Novel numerical technique for the second order Fredholm integro-differential equations using Bézier curves","authors":"Meltem Evrenosoğlu Adıyaman , Mustafa Kemal Altınbaş , Gülter Budakçı","doi":"10.1016/j.cam.2025.117249","DOIUrl":"10.1016/j.cam.2025.117249","url":null,"abstract":"<div><div>In this study, a novel approach is proposed to approximate the solution of second order Fredholm integro-differential equations. The proposed method extends the residual method used for solving ordinary differential equations. This method is based on approximating the solution of initial value problems using a Bézier curve. For the extension of the method, some novel formulas are derived to obtain the integral of the product of Bernstein basis functions and analytic functions. The proposed method is also applied to boundary value problems with minor modifications. The most significant feature of the proposed method is its ease of application to various problems, due to its simplicity and flexibility. Error analysis is provided for both initial and boundary value problems, demonstrating that this method achieves a high order of accuracy. In order to demonstrate the accuracy and efficiency of the method, several numerical examples are provided, and their results are compared with those obtained by other methods in the literature. The findings indicate that the proposed method is highly effective and can serve as a viable alternative to existing techniques for solving Fredholm integro-differential equations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"480 ","pages":"Article 117249"},"PeriodicalIF":2.6,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-11DOI: 10.1016/j.cam.2025.117252
Yiyi Tang
The Aït-Sahalia model is an important financial model. In past years, many variants of the Euler-Maruyama method are developed to simulate this SDE model. To derive the strong order one convergence, the Lamperti transformation is used. Then a challenge is that the derivative of the drift coefficient of the Lamperti-transformed Aït-Sahalia model has a pole at zero. The uniformly bounded inverse moments of the numerical solutions are useful to overcome this challenge. However, they are seldom studied in previous papers. In this paper, we will introduce a new numerical analysis technique to prove the uniformly bounded inverse moments of the projected Euler-Maruyama numerical solutions. Then we prove the -strong order one convergence of the projected Euler-Maruyama method. Moreover, the strong convergence theory is also established for the constant elasticity of volatility model and the Heston-3/2 volatility model.
{"title":"Strong order one convergence of the projected Euler-Maruyama method for scalar SDEs defined in the positive domain","authors":"Yiyi Tang","doi":"10.1016/j.cam.2025.117252","DOIUrl":"10.1016/j.cam.2025.117252","url":null,"abstract":"<div><div>The Aït-Sahalia model is an important financial model. In past years, many variants of the Euler-Maruyama method are developed to simulate this SDE model. To derive the strong order one convergence, the Lamperti transformation is used. Then a challenge is that the derivative of the drift coefficient of the Lamperti-transformed Aït-Sahalia model has a pole at zero. The uniformly bounded inverse moments of the numerical solutions are useful to overcome this challenge. However, they are seldom studied in previous papers. In this paper, we will introduce a new numerical analysis technique to prove the uniformly bounded inverse moments of the projected Euler-Maruyama numerical solutions. Then we prove the <span><math><msup><mi>L</mi><mi>r</mi></msup></math></span>-strong order one convergence of the projected Euler-Maruyama method. Moreover, the strong convergence theory is also established for the constant elasticity of volatility model and the Heston-3/2 volatility model.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"480 ","pages":"Article 117252"},"PeriodicalIF":2.6,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-10DOI: 10.1016/j.cam.2025.117248
Chuang Liang, Xiongbo Zheng, Xingzhou Jiang
We establish an efficient numerical method with respect to two-dimensional fractional diffusion equation. The proposed method employs a fourth-order compact difference scheme for discretizing in the space direction. In the time direction, the method uses a high-order L1-2 formula to discretize the Caputo derivative and introduces an infinitesimal term to generate a new alternating direction implicit (ADI) method. We provide the analysis of the unique solvability, stability and convergence of the method. Our method can achieve high-order convergence in both time and space directions, and the calculation speed is relatively faster. We use numerical illustrations to support the theoretical analysis results and show the effectiveness of the method.
{"title":"A kind of high order ADI method based on the L1-2 formula for fractional diffusion equation","authors":"Chuang Liang, Xiongbo Zheng, Xingzhou Jiang","doi":"10.1016/j.cam.2025.117248","DOIUrl":"10.1016/j.cam.2025.117248","url":null,"abstract":"<div><div>We establish an efficient numerical method with respect to two-dimensional fractional diffusion equation. The proposed method employs a fourth-order compact difference scheme for discretizing in the space direction. In the time direction, the method uses a high-order L1-2 formula to discretize the Caputo derivative and introduces an infinitesimal term to generate a new alternating direction implicit (ADI) method. We provide the analysis of the unique solvability, stability and convergence of the method. Our method can achieve high-order convergence in both time and space directions, and the calculation speed is relatively faster. We use numerical illustrations to support the theoretical analysis results and show the effectiveness of the method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"479 ","pages":"Article 117248"},"PeriodicalIF":2.6,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-09DOI: 10.1016/j.cam.2025.117245
Yu Shen, Xiangtuan Xiong
The electrophysiological process of catheter ablation for ventricular fibrillation treatment can be mathematically modeled as a Cauchy problem for the Laplace equation in an annular region, where boundary conditions are prescribed on the inner circumference. The potential and current density data are specified on the inner boundary, while our goal is to compute the potential on the outer boundary. This inverse boundary value problem is well-known in inverse problems for its severe ill-posedness, exhibiting extreme sensitivity to initial conditions and measurement noise. In this paper, we establish an a priori bound by constructing a periodic Sobolev space and derive Hölder-type error estimates for the approximate solution obtained through Tikhonov regularization at the outer boundary. According to the general regularization theory, this estimation is of order optimum. Furthermore, the numerical realization of this problem is discussed from two different perspectives: the Fourier expression obtained by singular value method and the matrix discretization. Simultaneously, representative numerical examples are provided, demonstrating the effectiveness of the method and superior performance through comparative results.
{"title":"Numerical solution and error estimation of Tikhonov regularization method for an annular inverse electrocardiography problem","authors":"Yu Shen, Xiangtuan Xiong","doi":"10.1016/j.cam.2025.117245","DOIUrl":"10.1016/j.cam.2025.117245","url":null,"abstract":"<div><div>The electrophysiological process of catheter ablation for ventricular fibrillation treatment can be mathematically modeled as a Cauchy problem for the Laplace equation in an annular region, where boundary conditions are prescribed on the inner circumference. The potential and current density data are specified on the inner boundary, while our goal is to compute the potential on the outer boundary. This inverse boundary value problem is well-known in inverse problems for its severe ill-posedness, exhibiting extreme sensitivity to initial conditions and measurement noise. In this paper, we establish an a priori bound by constructing a periodic Sobolev space and derive Hölder-type error estimates for the approximate solution obtained through Tikhonov regularization at the outer boundary. According to the general regularization theory, this estimation is of order optimum. Furthermore, the numerical realization of this problem is discussed from two different perspectives: the Fourier expression obtained by singular value method and the matrix discretization. Simultaneously, representative numerical examples are provided, demonstrating the effectiveness of the method and superior performance through comparative results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"479 ","pages":"Article 117245"},"PeriodicalIF":2.6,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-06DOI: 10.1016/j.cam.2025.117239
Fabio Cassini , Chiara Segala
In this manuscript, we study the turnpike property in stochastic discrete-time optimal control problems for interacting agents. Extending previous deterministic results, we show that the turnpike property persists in the presence of noise under suitable dissipativity and controllability conditions. To handle the possible stiffness in the system dynamics, we employ for the time discretization integrators of exponential type. Numerical experiments validate our findings, demonstrating the advantages of exponential integrators over standard explicit schemes and confirming the effectiveness of the turnpike control even in the stochastic setting.
{"title":"The turnpike control in stochastic multi-agent dynamics: A discrete-time approach with exponential integrators","authors":"Fabio Cassini , Chiara Segala","doi":"10.1016/j.cam.2025.117239","DOIUrl":"10.1016/j.cam.2025.117239","url":null,"abstract":"<div><div>In this manuscript, we study the turnpike property in stochastic discrete-time optimal control problems for interacting agents. Extending previous deterministic results, we show that the turnpike property persists in the presence of noise under suitable dissipativity and controllability conditions. To handle the possible stiffness in the system dynamics, we employ for the time discretization integrators of exponential type. Numerical experiments validate our findings, demonstrating the advantages of exponential integrators over standard explicit schemes and confirming the effectiveness of the turnpike control even in the stochastic setting.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"479 ","pages":"Article 117239"},"PeriodicalIF":2.6,"publicationDate":"2025-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-06DOI: 10.1016/j.cam.2025.117238
Akram Kohansal , Reza Pakyari
This paper develops comprehensive inference procedures for multi-component stress-strength reliability models with heterogeneous Dagum-distributed component strengths under adaptive hybrid progressive censoring (AHPC). We propose both classical and Bayesian estimation strategies, including maximum likelihood estimators (MLEs), asymptotic confidence intervals, approximate Bayesian estimators, and highest posterior density (HPD) credible intervals. A Markov chain Monte Carlo (MCMC) framework combined with Gibbs sampling is employed to handle complex posterior distributions efficiently. The methodology is validated through simulation studies and real-world data analysis, demonstrating the model’s flexibility in capturing heavy-tailed lifetime behavior and providing actionable insights for reliability planning, component selection, and preventive maintenance scheduling. The results highlight that incorporating AHPC schemes leads to improved estimation accuracy and practical adaptability in reliability engineering.
{"title":"Reliability assessment of heterogeneous Dagum-distributed multi-component stress-strength systems under adaptive hybrid progressive censoring","authors":"Akram Kohansal , Reza Pakyari","doi":"10.1016/j.cam.2025.117238","DOIUrl":"10.1016/j.cam.2025.117238","url":null,"abstract":"<div><div>This paper develops comprehensive inference procedures for multi-component stress-strength reliability models with heterogeneous Dagum-distributed component strengths under adaptive hybrid progressive censoring (AHPC). We propose both classical and Bayesian estimation strategies, including maximum likelihood estimators (MLEs), asymptotic confidence intervals, approximate Bayesian estimators, and highest posterior density (HPD) credible intervals. A Markov chain Monte Carlo (MCMC) framework combined with Gibbs sampling is employed to handle complex posterior distributions efficiently. The methodology is validated through simulation studies and real-world data analysis, demonstrating the model’s flexibility in capturing heavy-tailed lifetime behavior and providing actionable insights for reliability planning, component selection, and preventive maintenance scheduling. The results highlight that incorporating AHPC schemes leads to improved estimation accuracy and practical adaptability in reliability engineering.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"479 ","pages":"Article 117238"},"PeriodicalIF":2.6,"publicationDate":"2025-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145738825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-04DOI: 10.1016/j.cam.2025.117240
Florian Jarre
In this paper a fourth order asymptotically optimal error bound for a new cubic interpolating spline function, denoted by Q-spline, is derived for the case that only function values at given points are used but not any derivative information. The bound seems to be stronger than earlier error bounds for cubic spline interpolation in such setting such as the not-a-knot spline. A brief analysis of the conditioning of the end conditions of cubic spline interpolation leads to a modification of the not-a-knot spline, and some numerical examples suggest that the interpolation error of this revised not-a-knot spline generally is comparable to the near optimal Q-spline and lower than for the not-a-knot spline when the mesh size is small.
{"title":"Cubic spline functions revisited","authors":"Florian Jarre","doi":"10.1016/j.cam.2025.117240","DOIUrl":"10.1016/j.cam.2025.117240","url":null,"abstract":"<div><div>In this paper a fourth order asymptotically optimal error bound for a new cubic interpolating spline function, denoted by Q-spline, is derived for the case that only function values at given points are used but not any derivative information. The bound seems to be stronger than earlier error bounds for cubic spline interpolation in such setting such as the not-a-knot spline. A brief analysis of the conditioning of the end conditions of cubic spline interpolation leads to a modification of the not-a-knot spline, and some numerical examples suggest that the interpolation error of this revised not-a-knot spline generally is comparable to the near optimal Q-spline and lower than for the not-a-knot spline when the mesh size is small.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"478 ","pages":"Article 117240"},"PeriodicalIF":2.6,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145748388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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