This work deals with the offset fractional Fourier transform (OFrFT), which is a more general version of the fractional Fourier transform (FrFT). We demonstrate the basic properties such as translation, modulation and parity. The results are generalization of the FrFT properties. We study a relation of the OFrFT with the FrFT and the Fourier transform. Based on the relation, the key properties such as Parseval’s identity and inversion formula are derived. Applying the properties and the relation allow us to establish several versions of the uncertainty inequalities for the OFrFT. In addition, we discuss the comparison of the OFrFT with the FrFT in terms of properties and uncertainty principles. Finally, we perform an illustrative example to demonstrate that the value of Heisenberg uncertainty inequality for the OFrFT is bigger than that of Heisenberg uncertainty inequality for the FrFT and effect of the offset parameter in minimizing the Heisenberg uncertainty principle associated with the OFrFT.
{"title":"A comparative study on properties and uncertainty principles of fractional Fourier transform and offset fractional Fourier transform","authors":"Mawardi Bahri , Airien Nabilla B.A. , Nasrullah Bachtiar , Muhammad Zakir","doi":"10.1016/j.rinam.2025.100616","DOIUrl":"10.1016/j.rinam.2025.100616","url":null,"abstract":"<div><div>This work deals with the offset fractional Fourier transform (OFrFT), which is a more general version of the fractional Fourier transform (FrFT). We demonstrate the basic properties such as translation, modulation and parity. The results are generalization of the FrFT properties. We study a relation of the OFrFT with the FrFT and the Fourier transform. Based on the relation, the key properties such as Parseval’s identity and inversion formula are derived. Applying the properties and the relation allow us to establish several versions of the uncertainty inequalities for the OFrFT. In addition, we discuss the comparison of the OFrFT with the FrFT in terms of properties and uncertainty principles. Finally, we perform an illustrative example to demonstrate that the value of Heisenberg uncertainty inequality for the OFrFT is bigger than that of Heisenberg uncertainty inequality for the FrFT and effect of the offset parameter in minimizing the Heisenberg uncertainty principle associated with the OFrFT.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100616"},"PeriodicalIF":1.4,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654181","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 : 2025-08-01Epub Date: 2025-07-18DOI: 10.1016/j.rinam.2025.100615
Xiaofeng Li
This study presents the first analytical solution for wave propagation over composite seabeds integrating sinusoidal sandbars with truncated semi-elliptical topographies, overcoming limitations of conventional mild-slope equations in handling elliptical curvature effects, coupled Bragg scattering, and singularities at truncated boundaries. Utilizing Frobenius series expansion and multi-region field matching, we systematically quantify how geometric parameters— ratio, , and —govern wave reflection coefficients (). Key discoveries reveal that the ratio controls resonance peak frequencies (inducing 12% shifts per 0.1 change), the radius parameter triggers complete reflection () at a critical value of 0.5, and optimal expands reflection bandwidth by up to 22%. This work transcends classical studies on singular seabed types, establishes a theoretical foundation for designing wave-control metamaterials via multiscale resonances, and bridges classical potential flow theory with modern coastal engineering applications in wave energy harvesting, coastal protection, and offshore structure design.
{"title":"Multiscale wave resonance in composite sinusoidal-elliptical topographies: Critical transitions and analytical control","authors":"Xiaofeng Li","doi":"10.1016/j.rinam.2025.100615","DOIUrl":"10.1016/j.rinam.2025.100615","url":null,"abstract":"<div><div>This study presents the first analytical solution for wave propagation over composite seabeds integrating sinusoidal sandbars with truncated semi-elliptical topographies, overcoming limitations of conventional mild-slope equations in handling elliptical curvature effects, coupled Bragg scattering, and singularities at truncated boundaries. Utilizing Frobenius series expansion and multi-region field matching, we systematically quantify how geometric parameters—<span><math><mrow><mi>a</mi><mo>/</mo><mi>b</mi></mrow></math></span> ratio, <span><math><mrow><mi>δ</mi><mo>/</mo><mi>a</mi></mrow></math></span>, and <span><math><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>/</mo><mi>b</mi></mrow></math></span>—govern wave reflection coefficients (<span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span>). Key discoveries reveal that the <span><math><mrow><mi>a</mi><mo>/</mo><mi>b</mi></mrow></math></span> ratio controls resonance peak frequencies (inducing 12% shifts per 0.1 change), the radius parameter <span><math><mrow><mi>r</mi><mo>=</mo><mrow><mo>(</mo><msub><mrow><mi>h</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>−</mo><msub><mrow><mi>h</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mo>/</mo><msub><mrow><mi>h</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span> triggers complete reflection (<span><math><mrow><msub><mrow><mi>K</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>→</mo><mn>1</mn></mrow></math></span>) at a critical value of 0.5, and optimal <span><math><mrow><mi>δ</mi><mo>/</mo><mi>a</mi></mrow></math></span> expands reflection bandwidth by up to 22%. This work transcends classical studies on singular seabed types, establishes a theoretical foundation for designing wave-control metamaterials via multiscale resonances, and bridges classical potential flow theory with modern coastal engineering applications in wave energy harvesting, coastal protection, and offshore structure design.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100615"},"PeriodicalIF":1.4,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654180","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 : 2025-08-01Epub Date: 2025-07-17DOI: 10.1016/j.rinam.2025.100595
Mohammad Adm , Jürgen Garloff
A sign regular matrix is a matrix having the property that its non-zero minors of all orders have, for each order, an identical sign. Such matrices arise in a wide range of applications. In this paper, intervals of real matrices with respect to the usual entry-wise partial ordering are considered. Using variation diminution, it is shown that all matrices in such an interval are sign-regular with the same signature of their minors if a specified finite set of element matrices in the interval has this property.
{"title":"Variation diminution and intervals of sign regular matrices","authors":"Mohammad Adm , Jürgen Garloff","doi":"10.1016/j.rinam.2025.100595","DOIUrl":"10.1016/j.rinam.2025.100595","url":null,"abstract":"<div><div>A sign regular matrix is a matrix having the property that its non-zero minors of all orders have, for each order, an identical sign. Such matrices arise in a wide range of applications. In this paper, intervals of real matrices with respect to the usual entry-wise partial ordering are considered. Using variation diminution, it is shown that all matrices in such an interval are sign-regular with the same signature of their minors if a specified finite set of element matrices in the interval has this property.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100595"},"PeriodicalIF":1.4,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654176","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 : 2025-08-01Epub 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":"2025-08-01","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}
Pub Date : 2025-08-01Epub Date: 2025-08-27DOI: 10.1016/j.rinam.2025.100627
Kholmat Shadimetov , Anvar Adilkhodjaev , Otabek Gulomov
In this paper, we study the problem of constructing optimal formulas for approximate integration in the Sobolev space of periodic functions. Using the functional approach, we obtain optimal quadrature formulas for the approximate calculation of rapidly oscillating integrals. Then, we obtain explicit formulas for the coefficients of the optimal quadrature formulas and we get the sharp estimation of the error of the constructed formulas.
{"title":"Optimal quadrature formulas for approximate calculation of rapidly oscillating integrals","authors":"Kholmat Shadimetov , Anvar Adilkhodjaev , Otabek Gulomov","doi":"10.1016/j.rinam.2025.100627","DOIUrl":"10.1016/j.rinam.2025.100627","url":null,"abstract":"<div><div>In this paper, we study the problem of constructing optimal formulas for approximate integration in the Sobolev space <span><math><mrow><mover><mrow><msubsup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow><mrow><mfenced><mrow><mi>m</mi></mrow></mfenced></mrow></msubsup></mrow><mrow><mo>˜</mo></mrow></mover><mfenced><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow></mfenced></mrow></math></span> of periodic functions. Using the functional approach, we obtain optimal quadrature formulas for the approximate calculation of rapidly oscillating integrals. Then, we obtain explicit formulas for the coefficients of the optimal quadrature formulas and we get the sharp estimation of the error of the constructed formulas.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100627"},"PeriodicalIF":1.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144908279","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 : 2025-08-01Epub Date: 2025-07-28DOI: 10.1016/j.rinam.2025.100618
Takuto Kajimura, Yasunori Kimura
In this paper, we show some properties of a proximal mapping with a general perturbation for convex functions. We further investigate the existence and approximation of minimizers of a given convex function by using the proximal point algorithm with a general perturbation in complete geodesic spaces.
{"title":"The proximal point algorithm with a general perturbation on geodesic spaces","authors":"Takuto Kajimura, Yasunori Kimura","doi":"10.1016/j.rinam.2025.100618","DOIUrl":"10.1016/j.rinam.2025.100618","url":null,"abstract":"<div><div>In this paper, we show some properties of a proximal mapping with a general perturbation for convex functions. We further investigate the existence and approximation of minimizers of a given convex function by using the proximal point algorithm with a general perturbation in complete geodesic spaces.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100618"},"PeriodicalIF":1.4,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144712995","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 : 2025-08-01Epub Date: 2025-07-23DOI: 10.1016/j.rinam.2025.100613
Can Li , Xin Wang , Yubin Yan , Zexin Hou
In this paper, we consider a time semi-discrete scheme for a tempered subdiffusion equation with nonsmooth data. Due to the low regularity of the solution, the optimal convergence rate cannot be achieved when the L1 time-stepping scheme is directly applied to discretize the tempered fractional derivative. By introducing a correction term at the initial time step, we propose a corrected L1 scheme which recover to the optimal convergence rate. Theoretical error estimates and numerical experiments validate the improvement.
{"title":"A corrected L1 scheme for solving a tempered subdiffusion equation with nonsmooth data","authors":"Can Li , Xin Wang , Yubin Yan , Zexin Hou","doi":"10.1016/j.rinam.2025.100613","DOIUrl":"10.1016/j.rinam.2025.100613","url":null,"abstract":"<div><div>In this paper, we consider a time semi-discrete scheme for a tempered subdiffusion equation with nonsmooth data. Due to the low regularity of the solution, the optimal convergence rate cannot be achieved when the L1 time-stepping scheme is directly applied to discretize the tempered fractional derivative. By introducing a correction term at the initial time step, we propose a corrected L1 scheme which recover to the optimal convergence rate. Theoretical error estimates and numerical experiments validate the improvement.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100613"},"PeriodicalIF":1.4,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144687563","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 : 2025-08-01Epub Date: 2025-09-12DOI: 10.1016/j.rinam.2025.100634
Leonid Berezansky , Alexander Domoshnitsky
Explicit sufficient conditions for uniform exponential stability of two-dimensional linear vector integro-differential equations have been established. These criteria are novel and remain valid even in the special case of second-order linear ordinary vector differential equations. The proofs leverage the Bohl–Perron theorem, incorporate a priori estimates of solutions. An illustrative example is provided to demonstrate the applicability of the results.
{"title":"Stability for linear second order vector integro-differential equations","authors":"Leonid Berezansky , Alexander Domoshnitsky","doi":"10.1016/j.rinam.2025.100634","DOIUrl":"10.1016/j.rinam.2025.100634","url":null,"abstract":"<div><div>Explicit sufficient conditions for uniform exponential stability of two-dimensional linear vector integro-differential equations have been established. These criteria are novel and remain valid even in the special case of second-order linear ordinary vector differential equations. The proofs leverage the Bohl–Perron theorem, incorporate a priori estimates of solutions. An illustrative example is provided to demonstrate the applicability of the results.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100634"},"PeriodicalIF":1.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145044574","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 : 2025-08-01Epub Date: 2025-07-22DOI: 10.1016/j.rinam.2025.100608
Yujie Yun, Tieqiang Gang, Lijie Chen
In this study, we employ the iterative Linear Quadratic Gaussian (ILQG) method, discretized based on the high-order exponential Runge–Kutta methods, to numerically solve stochastic optimal control problems. In the sense of weak convergence, we derive a mean-square third-order scheme with an additive noise, and provide corresponding order conditions. As the analysis of order conditions is local, the analysis is transformed into a error estimate of the discrete problem with control constraints. Finally, the global control law is approximated by computing the node control via the ILQG method. The numerical experiment further demonstrates the significant stability of ILQG in dealing with stochastic semilinear control problems. The proposed approach presents the advantages of simplicity and efficiency.
{"title":"Discrete ILQG method based on high-order exponential Runge–Kutta discretization","authors":"Yujie Yun, Tieqiang Gang, Lijie Chen","doi":"10.1016/j.rinam.2025.100608","DOIUrl":"10.1016/j.rinam.2025.100608","url":null,"abstract":"<div><div>In this study, we employ the iterative Linear Quadratic Gaussian (ILQG) method, discretized based on the high-order exponential Runge–Kutta methods, to numerically solve stochastic optimal control problems. In the sense of weak convergence, we derive a mean-square third-order scheme with an additive noise, and provide corresponding order conditions. As the analysis of order conditions is local, the analysis is transformed into a <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span> error estimate of the discrete problem with control constraints. Finally, the global control law is approximated by computing the node control via the ILQG method. The numerical experiment further demonstrates the significant stability of ILQG in dealing with stochastic semilinear control problems. The proposed approach presents the advantages of simplicity and efficiency.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100608"},"PeriodicalIF":1.4,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144679589","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 : 2025-05-01Epub Date: 2025-03-10DOI: 10.1016/j.rinam.2025.100559
Ihor Borachok, Roman Chapko, Oksana Palianytsia
This paper presents the numerical solution of an initial boundary value problem for a parabolic Fredholm integro-differential equation (FIDE) in bounded 2D and 3D spatial domains. To reduce the dimensionality of the problem, we employ the Laguerre transformation and Rothe’s method, with both first- and second-order time discretization approximations. As a result, the time-dependent problem is transformed into a recurrent sequence of boundary value problems for elliptic FIDEs. The radial basis function (RBF) method is then applied, where each stationary solution is approximated as a linear combination of radial basis functions centered at specific points, along with polynomial basis functions. The placement of these center points is outlined for both two-dimensional and three-dimensional regions. Collocation at center points generates a sequence of linear systems with integral coefficients. To compute these coefficients numerically, parameterization is performed, and Gauss–Legendre and trapezoidal quadratures are used. The shape parameter of the RBFs is optimized through a real-coded genetic algorithm. Numerical results in both two-dimensional and three-dimensional domains confirm the effectiveness and applicability of the proposed approaches.
{"title":"On the numerical solution of a parabolic Fredholm integro-differential equation by the RBF method","authors":"Ihor Borachok, Roman Chapko, Oksana Palianytsia","doi":"10.1016/j.rinam.2025.100559","DOIUrl":"10.1016/j.rinam.2025.100559","url":null,"abstract":"<div><div>This paper presents the numerical solution of an initial boundary value problem for a parabolic Fredholm integro-differential equation (FIDE) in bounded 2D and 3D spatial domains. To reduce the dimensionality of the problem, we employ the Laguerre transformation and Rothe’s method, with both first- and second-order time discretization approximations. As a result, the time-dependent problem is transformed into a recurrent sequence of boundary value problems for elliptic FIDEs. The radial basis function (RBF) method is then applied, where each stationary solution is approximated as a linear combination of radial basis functions centered at specific points, along with polynomial basis functions. The placement of these center points is outlined for both two-dimensional and three-dimensional regions. Collocation at center points generates a sequence of linear systems with integral coefficients. To compute these coefficients numerically, parameterization is performed, and Gauss–Legendre and trapezoidal quadratures are used. The shape parameter of the RBFs is optimized through a real-coded genetic algorithm. Numerical results in both two-dimensional and three-dimensional domains confirm the effectiveness and applicability of the proposed approaches.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100559"},"PeriodicalIF":1.4,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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