Pub Date : 2025-07-09DOI: 10.1016/j.rinam.2025.100612
S. Zangoei Zadeh , M. Azizian , M. Sarvari
The Black–Scholes model, a powerful tool for valuation of equity options specially European equity options, is based on assumptions that are violated in some situations due to market realities. One of these cases is the instability of risk-free interest rates and the volatility of stock prices in the Black–Scholes model.
In this paper, in order to make the Black–Scholes model more in line with market realities, fixed parameters in the model, such as risk-free interest rates and stock price volatility, are considered with uncertainty. The obtained interval model is solved using discretization method and converting it into a minimization problem. Finally, The accuracy and efficiency of the method is tested by some numerical examples.
{"title":"An interval version of Black–Scholes European option pricing model and its numerical solution","authors":"S. Zangoei Zadeh , M. Azizian , M. Sarvari","doi":"10.1016/j.rinam.2025.100612","DOIUrl":"10.1016/j.rinam.2025.100612","url":null,"abstract":"<div><div>The Black–Scholes model, a powerful tool for valuation of equity options specially European equity options, is based on assumptions that are violated in some situations due to market realities. One of these cases is the instability of risk-free interest rates and the volatility of stock prices in the Black–Scholes model.</div><div>In this paper, in order to make the Black–Scholes model more in line with market realities, fixed parameters in the model, such as risk-free interest rates and stock price volatility, are considered with uncertainty. The obtained interval model is solved using discretization method and converting it into a minimization problem. Finally, The accuracy and efficiency of the method is tested by some numerical examples.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100612"},"PeriodicalIF":1.4,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144580081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-07-01DOI: 10.1016/j.rinam.2025.100609
Soumia EL OMARI, Said MELLIANI
This paper addresses proving that solutions exist for nonlinear elliptic problems characterized by boundary conditions of non-local type, as well as their uniqueness, within the framework of weighted Sobolev spaces. These problems are motivated by applications in petroleum engineering, where non-local boundary conditions model complex interactions in stratified reservoirs with three-dimensional geometries. Using the properties of Leray–Lions type operators, compactness arguments, and a priori estimates, we establish a fundamental theorem guaranteeing the existence of weak solutions under suitable assumptions. A rigorous proof of the uniqueness of solutions is also provided by exploiting the strict monotonicity of the operator. This work expands the modeling capabilities for contexts where non-local interactions play a key role, offering relevant mathematical tools for simulating oil well performance and other similar applications.
{"title":"Boundary conditions of nonlocal type in weighted Sobolev spaces for nonlinear elliptic problems","authors":"Soumia EL OMARI, Said MELLIANI","doi":"10.1016/j.rinam.2025.100609","DOIUrl":"10.1016/j.rinam.2025.100609","url":null,"abstract":"<div><div>This paper addresses proving that solutions exist for nonlinear elliptic problems characterized by boundary conditions of non-local type, as well as their uniqueness, within the framework of weighted Sobolev spaces. These problems are motivated by applications in petroleum engineering, where non-local boundary conditions model complex interactions in stratified reservoirs with three-dimensional geometries. Using the properties of Leray–Lions type operators, compactness arguments, and a priori estimates, we establish a fundamental theorem guaranteeing the existence of weak solutions under suitable assumptions. A rigorous proof of the uniqueness of solutions is also provided by exploiting the strict monotonicity of the operator. This work expands the modeling capabilities for contexts where non-local interactions play a key role, offering relevant mathematical tools for simulating oil well performance and other similar applications.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100609"},"PeriodicalIF":1.4,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144517410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-06-27DOI: 10.1016/j.rinam.2025.100603
Yutaka Sakuma, Yan Linn Aung
In this paper, we consider an queue, where arriving customers decide whether to join the queue or not join based on the queue length at arrival instants. Kerner (2008, Stochastic Models) studies the queue, and derives a recursive formula for the Laplace-Stieltjes transform (LST, for short) of the conditional distribution of the server’s residual service time, given the queue length at arrival instants. This paper aims to analyze the queue in a much simpler way than the previous studies, and to show that our LST of the conditional distribution of the server’s residual service time is given in a more numerically stable form than that of the previous studies, specifically by avoiding the indeterminate form such as . We then use the formula to compute the customers joining probabilities in Nash equilibrium.
{"title":"A numerically stable formula for the conditional distribution of the residual service time in the Mn/PH/1 queue","authors":"Yutaka Sakuma, Yan Linn Aung","doi":"10.1016/j.rinam.2025.100603","DOIUrl":"10.1016/j.rinam.2025.100603","url":null,"abstract":"<div><div>In this paper, we consider an <span><math><mrow><msub><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>/</mo><mi>P</mi><mi>H</mi><mo>/</mo><mn>1</mn></mrow></math></span> queue, where arriving customers decide whether to join the queue or not join based on the queue length at arrival instants. Kerner (2008, <em>Stochastic Models</em>) studies the <span><math><mrow><msub><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>/</mo><mi>G</mi><mo>/</mo><mn>1</mn></mrow></math></span> queue, and derives a recursive formula for the Laplace-Stieltjes transform (LST, for short) of the conditional distribution of the server’s residual service time, given the queue length at arrival instants. This paper aims to analyze the <span><math><mrow><msub><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>/</mo><mi>P</mi><mi>H</mi><mo>/</mo><mn>1</mn></mrow></math></span> queue in a much simpler way than the previous studies, and to show that our LST of the conditional distribution of the server’s residual service time is given in a more numerically stable form than that of the previous studies, specifically by avoiding the indeterminate form such as <span><math><mrow><mn>0</mn><mo>/</mo><mn>0</mn></mrow></math></span>. We then use the formula to compute the customers joining probabilities in Nash equilibrium.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100603"},"PeriodicalIF":1.4,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144500879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper focuses on the portfolio optimization problem in the presence of the European options in the illiquid market. To do this, we extract the features of the market data using the statistical test to design a general financial model. After that, applying the dynamic replicating portfolio strategy, we derive a comprehensive partial integral differential equation for European option pricing in the illiquid market where the jump part of the model follows the empirical distribution. Since the structure of the equation is complex, we use the finite difference method to solve it. Furthermore, we apply the MCVaR portfolio optimization model with the short selling constraint to obtain the optimal portfolio strategy according to the risk tolerance amounts of the investors. Finally, we find the optimal portfolio under different amounts of the model’s parameters based on the S&P market data.
{"title":"Portfolio optimization in the illiquid market using the empirical distribution","authors":"Pouya Fakhraeipour, Farshid Mehrdoust, Alireza Najafi","doi":"10.1016/j.rinam.2025.100611","DOIUrl":"10.1016/j.rinam.2025.100611","url":null,"abstract":"<div><div>This paper focuses on the portfolio optimization problem in the presence of the European options in the illiquid market. To do this, we extract the features of the market data using the statistical test to design a general financial model. After that, applying the dynamic replicating portfolio strategy, we derive a comprehensive partial integral differential equation for European option pricing in the illiquid market where the jump part of the model follows the empirical distribution. Since the structure of the equation is complex, we use the finite difference method to solve it. Furthermore, we apply the MCVaR portfolio optimization model with the short selling constraint to obtain the optimal portfolio strategy according to the risk tolerance amounts of the investors. Finally, we find the optimal portfolio under different amounts of the model’s parameters based on the S&P market data.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100611"},"PeriodicalIF":1.4,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144500878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-06-25DOI: 10.1016/j.rinam.2025.100606
HanLin Li, Jiang Zhou
This paper proves the weak type estimates of the Hardy–Littlewood maximal operator on local Morrey spaces associated with ball quasi-Banach function spaces. As an application, we further obtain the weak type estimates of the Hardy–Littlewood maximal operator on the local Morrey spaces with variable exponents and the homogeneous Herz-type spaces with variable exponents.
{"title":"Weak type estimates of Hardy–Littlewood maximal operator on local Morrey spaces associated with ball quasi-Banach function spaces","authors":"HanLin Li, Jiang Zhou","doi":"10.1016/j.rinam.2025.100606","DOIUrl":"10.1016/j.rinam.2025.100606","url":null,"abstract":"<div><div>This paper proves the weak type estimates of the Hardy–Littlewood maximal operator on local Morrey spaces associated with ball quasi-Banach function spaces. As an application, we further obtain the weak type estimates of the Hardy–Littlewood maximal operator on the local Morrey spaces with variable exponents and the homogeneous Herz-type spaces with variable exponents.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100606"},"PeriodicalIF":1.4,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144471263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the Galerkin method for obtaining approximate solutions to linear Fredholm integral equations of the second kind. The finite element solution is represented as a linear combination of basis functions, and the construction of suitable basis functions plays a crucial role in the accuracy of the approximation. We propose an optimal interpolation formula that exactly reproduces the functions and , and derive basis functions from its coefficients. This interpolation formula is constructed within the Hilbert space . To evaluate the effectiveness of the proposed approach, we solve several integral equations using the Galerkin method with two types of basis functions: the newly constructed exponential basis and classical piecewise linear basis functions. Numerical experiments are presented to compare the accuracy of these approaches. Graphs and tables illustrate the approximation errors, demonstrating that both basis functions achieve an error order of , with the optimal interpolation-based basis yielding superior accuracy in certain cases.
{"title":"The numerical solution of a Fredholm integral equation of the second kind using the Galerkin method based on optimal interpolation","authors":"Samandar Babaev , Abdullo Hayotov , Asliddin Boltaev , Surayyo Mirzoyeva , Malika Mirzaeva","doi":"10.1016/j.rinam.2025.100607","DOIUrl":"10.1016/j.rinam.2025.100607","url":null,"abstract":"<div><div>In this paper, we study the Galerkin method for obtaining approximate solutions to linear Fredholm integral equations of the second kind. The finite element solution is represented as a linear combination of basis functions, and the construction of suitable basis functions plays a crucial role in the accuracy of the approximation. We propose an optimal interpolation formula that exactly reproduces the functions <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>x</mi></mrow></msup></math></span> and <span><math><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>x</mi></mrow></msup></math></span>, and derive basis functions from its coefficients. This interpolation formula is constructed within the Hilbert space <span><math><msubsup><mrow><mi>W</mi></mrow><mrow><mn>2</mn></mrow><mrow><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mrow></msubsup></math></span>. To evaluate the effectiveness of the proposed approach, we solve several integral equations using the Galerkin method with two types of basis functions: the newly constructed exponential basis and classical piecewise linear basis functions. Numerical experiments are presented to compare the accuracy of these approaches. Graphs and tables illustrate the approximation errors, demonstrating that both basis functions achieve an error order of <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>h</mi><mo>)</mo></mrow></mrow></math></span>, with the optimal interpolation-based basis yielding superior accuracy in certain cases.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100607"},"PeriodicalIF":1.4,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144338603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-06-20DOI: 10.1016/j.rinam.2025.100605
Guoqiang Zhao, Dongxi Li
Cancer subtype analysis faces challenges due to limited availability of gene samples and the complexity of cancer gene expression data. The imbalance of Positive and negative category ratio and high-dimensional redundant information degrade prediction performance. This paper proposes an integrated extreme random forest with feature selection model TreeEM(Tree-enhanced Ensemble Model combining with feature selection) to enhance prediction ability and reduce computational costs. The TreeEM model combines the Max-Relevance and Min-Redundancy(MRMR) feature selection method with improved fusion undersampling random forest and extreme tree forest. The TreeEM model achieves excellent performance on three cancer datasets, especially on the multi-omics datasets BRCA(Breast Cancer) and ARCENE datasets, with average improvements of 7.90% and 1.90% in prediction accuracy, respectively. This model also uses TCGA data with known survival time for survival analysis and prediction, demonstrating the reliability of the TreeEM model. This work contributes to advancements in computational tools for cancer research, facilitating precision medicine approaches and improving decision-making. The above results provide new ideas for cancer subtype classification, but the existing methods still have limitations in data imbalance and high-dimensional feature processing. In the following section, the shortcomings of the current research and the innovative solutions of this paper are systematically described.
由于基因样本的有限可用性和癌症基因表达数据的复杂性，癌症亚型分析面临挑战。正负类比失衡和高维冗余信息会降低预测性能。为了提高预测能力和降低计算成本，本文提出了一种带有特征选择模型TreeEM（Tree-enhanced Ensemble model and feature selection）的集成极端随机森林模型。该模型将最大相关和最小冗余（MRMR）特征选择方法与改进的融合欠采样随机森林和极端树森林相结合。TreeEM模型在三个癌症数据集上取得了优异的表现，特别是在多组学数据集BRCA（Breast cancer）和ARCENE数据集上，预测准确率平均分别提高了7.90%和1.90%。该模型还使用已知生存时间的TCGA数据进行生存分析和预测，证明了TreeEM模型的可靠性。这项工作有助于癌症研究的计算工具的进步，促进精准医学方法和改进决策。上述结果为癌症亚型分类提供了新的思路，但现有方法在数据不平衡、高维特征处理等方面仍存在局限性。在接下来的部分中，系统地描述了当前研究的不足和本文的创新解决方案。
{"title":"TreeEM: Tree-enhanced ensemble model combining with feature selection for cancer subtype classification and survival prediction","authors":"Guoqiang Zhao, Dongxi Li","doi":"10.1016/j.rinam.2025.100605","DOIUrl":"10.1016/j.rinam.2025.100605","url":null,"abstract":"<div><div>Cancer subtype analysis faces challenges due to limited availability of gene samples and the complexity of cancer gene expression data. The imbalance of Positive and negative category ratio and high-dimensional redundant information degrade prediction performance. This paper proposes an integrated extreme random forest with feature selection model TreeEM(Tree-enhanced Ensemble Model combining with feature selection) to enhance prediction ability and reduce computational costs. The TreeEM model combines the Max-Relevance and Min-Redundancy(MRMR) feature selection method with improved fusion undersampling random forest and extreme tree forest. The TreeEM model achieves excellent performance on three cancer datasets, especially on the multi-omics datasets BRCA(Breast Cancer) and ARCENE datasets, with average improvements of 7.90% and 1.90% in prediction accuracy, respectively. This model also uses TCGA data with known survival time for survival analysis and prediction, demonstrating the reliability of the TreeEM model. This work contributes to advancements in computational tools for cancer research, facilitating precision medicine approaches and improving decision-making. The above results provide new ideas for cancer subtype classification, but the existing methods still have limitations in data imbalance and high-dimensional feature processing. In the following section, the shortcomings of the current research and the innovative solutions of this paper are systematically described.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100605"},"PeriodicalIF":1.4,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-06-18DOI: 10.1016/j.rinam.2025.100602
Pengfei Luo , Yun Zhang , Lu Xu
The directional motivation of predator is influenced by the density of prey and its alarm call, this paper focuses on a three-species spatial intraguild predation model involving prey-taxis and alarm-taxis. By energy estimates and heat semigroup theory, we prove that this model possesses a bounded and global classical solution in -dimensional space () with Neumann boundary conditions.
{"title":"Global boundedness of a three-species spatial intraguild predation model with alarm-taxis","authors":"Pengfei Luo , Yun Zhang , Lu Xu","doi":"10.1016/j.rinam.2025.100602","DOIUrl":"10.1016/j.rinam.2025.100602","url":null,"abstract":"<div><div>The directional motivation of predator is influenced by the density of prey and its alarm call, this paper focuses on a three-species spatial intraguild predation model involving prey-taxis and alarm-taxis. By energy estimates and heat semigroup theory, we prove that this model possesses a bounded and global classical solution in <span><math><mi>N</mi></math></span>-dimensional space (<span><math><mrow><mi>N</mi><mo>≥</mo><mn>3</mn></mrow></math></span>) with Neumann boundary conditions.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100602"},"PeriodicalIF":1.4,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144307320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-06-16DOI: 10.1016/j.rinam.2025.100599
Jean-Baptiste Leroux, Matthieu Sacher
Five non-tabulated integrals are analytically calculated. These integrals emerge from the linear theory of partially cavitating hydrofoils and propeller blades. They appear in a series of weight functions involved in the determination of the cavitation number and cavity shape. The present analytical results eliminate the need for unnecessary numerical integrations, which could be beneficial in reducing computational costs and improving the robustness of numerical models.
{"title":"Analytical computation of five unresolved integrals in the linear theory of partially cavitating hydrofoils","authors":"Jean-Baptiste Leroux, Matthieu Sacher","doi":"10.1016/j.rinam.2025.100599","DOIUrl":"10.1016/j.rinam.2025.100599","url":null,"abstract":"<div><div>Five non-tabulated integrals are analytically calculated. These integrals emerge from the linear theory of partially cavitating hydrofoils and propeller blades. They appear in a series of weight functions involved in the determination of the cavitation number and cavity shape. The present analytical results eliminate the need for unnecessary numerical integrations, which could be beneficial in reducing computational costs and improving the robustness of numerical models.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100599"},"PeriodicalIF":1.4,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144298102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-06-16DOI: 10.1016/j.rinam.2025.100604
Cheng Chen , Wenting Shao
For solving the KdV equation, a novel numerical method with high order accuracy in both space and time is proposed. In the spatial direction, Sinc collocation method, which has the property of exponential convergence, is adopted. In the temporal direction, the variable stepsize Runge–Kutta-embedded pair RKq(p) is utilized. Sinc collocation method is applicable when the approximated function satisfies the exponential decay as the spatial variable tends to infinity, this characteristic is consistent with the one of the soliton solution of the KdV equation. For practical computation, a sufficiently large finite domain is taken, on which the differential matrices with respect to the discrete points are constructed. A new adaptive strategy is proposed to enhance the robustness of the variable stepsize algorithm. In the numerical experiment, four embedded pairs including RK5(4), RK6(5), RK8(7) and RK9(8) are investigated in terms of accuracy, CPU time, the minimum, average and maximum time stepsizes. The numerical results show that RK8(7) has a better performance in the computational efficiency, it achieves higher accuracy with significantly less CPU time. Besides, the KdV-Burgers equation with nonhomogeneous Dirichlet boundary condition imposed on a general interval is considered. The single-exponential transformation and double-exponential transformation are involved. We show that Sinc collocation method, enhanced by exponential transformations, provides an effective numerical approximation for this problem.
{"title":"A kind of adaptive variable stepsize embedded Runge–Kutta pairs coupled with the Sinc collocation method for solving the KdV equation","authors":"Cheng Chen , Wenting Shao","doi":"10.1016/j.rinam.2025.100604","DOIUrl":"10.1016/j.rinam.2025.100604","url":null,"abstract":"<div><div>For solving the KdV equation, a novel numerical method with high order accuracy in both space and time is proposed. In the spatial direction, Sinc collocation method, which has the property of exponential convergence, is adopted. In the temporal direction, the variable stepsize Runge–Kutta-embedded pair RKq(p) is utilized. Sinc collocation method is applicable when the approximated function satisfies the exponential decay as the spatial variable tends to infinity, this characteristic is consistent with the one of the soliton solution of the KdV equation. For practical computation, a sufficiently large finite domain is taken, on which the differential matrices with respect to the discrete points are constructed. A new adaptive strategy is proposed to enhance the robustness of the variable stepsize algorithm. In the numerical experiment, four embedded pairs including RK5(4), RK6(5), RK8(7) and RK9(8) are investigated in terms of accuracy, CPU time, the minimum, average and maximum time stepsizes. The numerical results show that RK8(7) has a better performance in the computational efficiency, it achieves higher accuracy with significantly less CPU time. Besides, the KdV-Burgers equation with nonhomogeneous Dirichlet boundary condition imposed on a general interval is considered. The single-exponential transformation and double-exponential transformation are involved. We show that Sinc collocation method, enhanced by exponential transformations, provides an effective numerical approximation for this problem.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100604"},"PeriodicalIF":1.4,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144291511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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