Mathematical Methods in the Applied Sciences最新文献_第2页

Special Affine Fourier Transform on Tempered Distribution and Its Application

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-01-26 DOI: 10.1002/mma.10657

Manish Kumar, Bhawna

{"title":"Special Affine Fourier Transform on Tempered Distribution and Its Application","authors":"Manish Kumar,  Bhawna","doi":"10.1002/mma.10657","DOIUrl":"https://doi.org/10.1002/mma.10657","url":null,"abstract":"<div>\u0000 \u0000 <p>The main aim of this work is to develop a theoretical framework for generalized pseudo-differential operators involving the special affine Fourier transform (SAFT), associated with a symbol \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>δ</mi>\u0000 <mo>(</mo>\u0000 <mi>μ</mi>\u0000 <mo>,</mo>\u0000 <mi>η</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ delta left(mu, eta right) $$</annotation>\u0000 </semantics></math>. Some important properties of the SAFT are established, and it is proved that the product of two generalized pseudo-differential operators is shown to be a generalized pseudo-differential operator. Further, we explore the practical applications of the SAFT in solving generalized partial differential equations, such as the generalized telegraph and wave equations, providing closed-form solutions. Furthermore, graphical visualizations for these solutions are illustrated via MATLAB R2023b.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"6092-6102"},"PeriodicalIF":2.1,"publicationDate":"2025-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Infinitely Many Sign-Changing Solutions for a Schrödinger Equation With Competing Potentials

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-01-26 DOI: 10.1002/mma.10727

Ke Wu, Kaijing Cheng, Fen Zhou

{"title":"Infinitely Many Sign-Changing Solutions for a Schrödinger Equation With Competing Potentials","authors":"Ke Wu, Kaijing Cheng, Fen Zhou","doi":"10.1002/mma.10727","DOIUrl":"https://doi.org/10.1002/mma.10727","url":null,"abstract":"<div>\u0000 \u0000 <p>Consider the following nonlinear problem with competing potentials: \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mi>Δ</mi>\u0000 <mi>u</mi>\u0000 <mo>+</mo>\u0000 <mi>P</mi>\u0000 <mo>(</mo>\u0000 <mo>|</mo>\u0000 <mi>y</mi>\u0000 <mo>|</mo>\u0000 <mo>)</mo>\u0000 <mi>u</mi>\u0000 <mo>=</mo>\u0000 <mi>Q</mi>\u0000 <mo>(</mo>\u0000 <mo>|</mo>\u0000 <mi>y</mi>\u0000 <mo>|</mo>\u0000 <mo>)</mo>\u0000 <mo>|</mo>\u0000 <mi>u</mi>\u0000 <msup>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mi>u</mi>\u0000 <mo>,</mo>\u0000 <mtext>in</mtext>\u0000 <mspace></mspace>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ -Delta u&#x0002B;Pleft(&#x0007C;y|right)u&#x0003D;Qleft(&#x0007C;y|right){left&#x0007C;uright&#x0007C;}&#x0005E;{p-1}u,mathrm{in}kern0.3em {mathbb{R}}&#x0005E;N $$</annotation>\u0000 </semantics></math>, where \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>≥</mo>\u0000 <mn>3</mn>\u0000 <mo>,</mo>\u0000 <mspace></mspace>\u0000 <mn>1</mn>\u0000 <mo><</mo>\u0000 <mi>p</mi>\u0000 <mo><</mo>\u0000 <mfrac>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>+</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>−</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mfrac>\u0000 </mrow>\u0000 <annotation>$$ Nge 3,kern0.3em 1&lt;p&lt;frac{N&#x0002B;2}{N-2} $$</annotation>\u0000 </semantics></math>, and \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 <mo>(</mo>\u0000 <mo>|</mo>\u0000 <mi>y</mi>\u0000 <mo>|</mo>\u0000 <mo>)</mo>\u0000 <mo>,</mo>\u0000 <mspace></mspace>\u0000 <mi>Q</mi>\u0000 <mo>(</mo>\u0000 <mo>|</mo>\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6918-6929"},"PeriodicalIF":2.1,"publicationDate":"2025-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Radial Basis Function-Hermite Finite Difference Method for the Two-Dimensional Distributed-Order Time-Fractional Cable Equation

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-01-23 DOI: 10.1002/mma.10696

Majid Haghi, Mohammad Ilati

{"title":"A Radial Basis Function-Hermite Finite Difference Method for the Two-Dimensional Distributed-Order Time-Fractional Cable Equation","authors":"Majid Haghi, Mohammad Ilati","doi":"10.1002/mma.10696","DOIUrl":"https://doi.org/10.1002/mma.10696","url":null,"abstract":"<div>\u0000 \u0000 <p>In this article, our main objective is to propose a high-order local meshless method for numerical solution of two-dimensional distributed-order time-fractional cable equation on both regular and irregular domains. First, the distribution-order integral is approximated by the Gauss-Legendre quadrature formula, and then a second-order weighted and shifted Grünwald difference (WSGD) scheme is applied to approximate the time Riemann-Liouville derivatives. The stability and convergence analysis of the time-discrete outline are investigated by the energy approach. The spatial dimension of the model is discretized by the fourth-order local radial basis function-Hermite finite difference (RBF-HFD) method. Some numerical experiments are performed on regular and irregular computational domains to verify the ability, efficiency, and accuracy of the proposed numerical procedure. The numerical simulations clearly demonstrate the high accuracy of the provided numerical process in comparison to existing procedures. Finally, it can be concluded that the presented technique is a suitable alternative to the existing numerical techniques for the distributed-order time-fractional cable equation.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6573-6585"},"PeriodicalIF":2.1,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Effect of Nonlinearities With Arbitrary-Order Derivatives on Dynamic Transitions

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-01-23 DOI: 10.1002/mma.10709

Taylan Şengül, Burhan Tiryakioglu

{"title":"The Effect of Nonlinearities With Arbitrary-Order Derivatives on Dynamic Transitions","authors":"Taylan Şengül, Burhan Tiryakioglu","doi":"10.1002/mma.10709","DOIUrl":"https://doi.org/10.1002/mma.10709","url":null,"abstract":"<div>\u0000 \u0000 <p>The primary objective of this paper is to classify the first transitions of a general class of one spatial dimensional nonlinear partial differential equations on a bounded interval. The linear part of the equation is assumed to have a real discrete spectrum with a complete set of eigenfunctions, which are of the form \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>sin</mi>\u0000 <mi>k</mi>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 <annotation>$$ sin kx $$</annotation>\u0000 </semantics></math> or \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>cos</mi>\u0000 <mi>k</mi>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mspace></mspace>\u0000 <mi>k</mi>\u0000 <mo>∈</mo>\u0000 <mi>ℕ</mi>\u0000 </mrow>\u0000 <annotation>$$ cos kx,kern0.3em kin mathbb{N} $$</annotation>\u0000 </semantics></math>. The nonlinear operator consists of arbitrary finite products and sums of the unknown function and its derivatives of arbitrary order. The equations allow for a trivial steady-state solution that becomes unstable when a control parameter exceeds a certain threshold. Unlike most of the previous research in this direction that considers specific equations, this general framework is suitable for extension in several directions such as the higher spatial dimensions and different basis vectors. Under a set of assumptions that are often valid in many interesting applications, we derive two numbers called the transition number and the critical index which completely describe the first dynamic transition. We make detailed numerical computations that reveal the properties of the transition numbers. To show the applicability of our theoretical results, we determine the first transitions of several well-known equations including the Cahn–Hilliard, thin film, Harry Dym, Kawamoto, and Rosenau–Hyman equations.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6704-6716"},"PeriodicalIF":2.1,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Semigroup Dynamics and Chaotic Behavior in Second-Order Partial Differential Equations on H1×L2 Space

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-01-23 DOI: 10.1002/mma.10675

Manal Menchih, Khalid Hilal, Ahmed Kajouni

{"title":"Semigroup Dynamics and Chaotic Behavior in Second-Order Partial Differential Equations on \u0000H1×L2 Space","authors":"Manal Menchih, Khalid Hilal, Ahmed Kajouni","doi":"10.1002/mma.10675","DOIUrl":"https://doi.org/10.1002/mma.10675","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper focuses on the dynamics of a second-order partial differential equation within the space \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {L}&#x0005E;2 $$</annotation>\u0000 </semantics></math> described by \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mfrac>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>∂</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mi>ϑ</mi>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>∂</mi>\u0000 <msup>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 </mfrac>\u0000 <mo>+</mo>\u0000 <mi>a</mi>\u0000 <mfrac>\u0000 <mrow>\u0000 <mi>∂</mi>\u0000 <mi>ϑ</mi>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>∂</mi>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </mfrac>\u0000 <mo>+</mo>\u0000 <mi>b</mi>\u0000 <mi>ϑ</mi>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mi>c</mi>\u0000 <mfrac>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>∂</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mi>ϑ</mi>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6335-6341"},"PeriodicalIF":2.1,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Using Moving Least Square With Particle Swarm Optimization to Solve Nonlinear Transient Convective–Radiative Heat Transfer Problems in the Existence of a Magnetic Field

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-01-22 DOI: 10.1002/mma.10650

M. J. Mahmoodabadi, M. Atashafrooz, M. Yousef Ibrahim

{"title":"Using Moving Least Square With Particle Swarm Optimization to Solve Nonlinear Transient Convective–Radiative Heat Transfer Problems in the Existence of a Magnetic Field","authors":"M. J. Mahmoodabadi, M. Atashafrooz, M. Yousef Ibrahim","doi":"10.1002/mma.10650","DOIUrl":"https://doi.org/10.1002/mma.10650","url":null,"abstract":"<div>\u0000 \u0000 <p>In the current research, a novel hybrid scheme is proposed to solve nonlinear equations arising in heat transfer through the combination of meta-heuristic algorithms and interpolation methods. In order to define a proper objective function for minimization by particle swarm optimization (PSO), the constrained problem is converted into an unconstrained one through the penalty method. Furthermore, the moving least square (MLS) technique is implemented to interpolate and approximate the derivatives appeared in the equation. The main problem for challenging this combined scheme is nonlinear transient convective–radiative heat transfer in existence of a magnetic field. To study the efficiency of the MLS, the results would be contrasted with those extracted by a finite difference method (FDM) based PSO approach. Through five distinctive examples, the evolutionary diagrams as well as temperature distributions found by different methods are displayed, and the effects of the constant parameters are investigated. Besides, the simulations of this research work clearly depict good agreements of the numerical results obtained by the suggested idea with those reported in literature.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5987-5997"},"PeriodicalIF":2.1,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Infinitely Many Positive Nonradial Solutions for the Kirchhoff Equation

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-01-22 DOI: 10.1002/mma.10718

Hui Guo, Boling Tang, Tao Wang

{"title":"Infinitely Many Positive Nonradial Solutions for the Kirchhoff Equation","authors":"Hui Guo, Boling Tang, Tao Wang","doi":"10.1002/mma.10718","DOIUrl":"https://doi.org/10.1002/mma.10718","url":null,"abstract":"<div>\u0000 \u0000 <p>We are concerned with the existence of positive nonradial solutions to the following Kirchhoff equation: \u0000\u0000 </p><div><span>\u0000 <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mtable>\u0000 <mtr>\u0000 <mtd>\u0000 <mo>−</mo>\u0000 <mspace></mspace>\u0000 <mfenced>\u0000 <mrow>\u0000 <mi>a</mi>\u0000 <mo>+</mo>\u0000 <mi>b</mi>\u0000 <msub>\u0000 <mrow>\u0000 <mo>∫</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 </msub>\u0000 <mo>|</mo>\u0000 <mo>∇</mo>\u0000 <mi>u</mi>\u0000 <msup>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mi>d</mi>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 <mi>Δ</mi>\u0000 <mi>u</mi>\u0000 <mo>+</mo>\u0000 <mi>V</mi>\u0000 <mo>(</mo>\u0000 <mo>|</mo>\u0000 <mi>x</mi>\u0000 <mo>|</mo>\u0000 <mo>)</mo>\u0000 <mi>u</mi>\u0000 <mo>=</mo>\u0000 <mi>Q</mi>\u0000 <mo>(</mo>\u0000 <mo>|</mo>\u0000 <mi>x</mi>\u0000 <mo>|</mo>\u0000 <mo>)</mo>\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6830-6843"},"PeriodicalIF":2.1,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

G-Convergence of Friedrichs Systems Revisited

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-01-22 DOI: 10.1002/mma.10656

K. Burazin, M. Erceg, M. Waurick

引用次数: 0

Exponential Stability of Higher Order Fractional Neutral Stochastic Differential Equation Via Integral Contractors

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-01-22 DOI: 10.1002/mma.10681

Dimplekumar N. Chalishajar, Dhanalakshmi Kasinathan, Ramkumar Kasinathan, Ravikumar Kasinathan

{"title":"Exponential Stability of Higher Order Fractional Neutral Stochastic Differential Equation Via Integral Contractors","authors":"Dimplekumar N. Chalishajar, Dhanalakshmi Kasinathan, Ramkumar Kasinathan, Ravikumar Kasinathan","doi":"10.1002/mma.10681","DOIUrl":"https://doi.org/10.1002/mma.10681","url":null,"abstract":"<p>The well-posedness results for mild solutions to the fractional neutral stochastic differential system with Rosenblatt process with Hurst index \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ĥ</mi>\u0000 <mo>∈</mo>\u0000 <mfenced>\u0000 <mrow>\u0000 <mfrac>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mfrac>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 <annotation>$$ hat{H}in left(frac{1}{2},1right) $$</annotation>\u0000 </semantics></math> is discussed in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and sequencing technique. In contrast to previous publications, we do not need to specify the induced inverse of the controllability operator to prove the stability results, and the relevant nonlinear function does not have to meet the Lipschitz condition. Furthermore, exponential stability results for neutral stochastic differential systems with Poisson jump have been established. Finally, an application to demonstrate the acquired results is discussed. We demonstrate the fractional Zener model for wave equation obeying the viscoelastic materials as a practical application of the system studied, which is a generalization of classical wave equation.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6425-6446"},"PeriodicalIF":2.1,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10681","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Deterministic, Stochastic, and Deep Learning Approaches to Understand the Economic Fluctuations in India

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-01-20 DOI: 10.1002/mma.10700

Saptaporni Karmakar, Arkaprovo Chakraborty

{"title":"Deterministic, Stochastic, and Deep Learning Approaches to Understand the Economic Fluctuations in India","authors":"Saptaporni Karmakar, Arkaprovo Chakraborty","doi":"10.1002/mma.10700","DOIUrl":"https://doi.org/10.1002/mma.10700","url":null,"abstract":"<div>\u0000 \u0000 <p>In the present work, a new mathematical framework is proposed for studying the interrelation among population growth rate, GDP, inflation rate, and unemployment rate within deterministic and stochastic frameworks. The values of the parameters of the proposed model are estimated using real data from India. The local and global uniqueness of solutions is established for the stochastic model. The deterministic model is solved by using the Adams-Bashforth-Moulton predictor-corrector method, and Milstein's method is used for solving the stochastic model. Numerical simulations correlated quite strongly with observed data, while projections for the 2024–2030 period indicate that controlled population growth bodes well for the outlook of the economy for India, supporting economic prosperity alongside reduced inflation and better employment conditions. The findings presented in this work are correlational; therefore, to find the possible cause for this phenomenon, further research is required with detailed datasets. Comparing our model's GDP predictions with that obtained using a long short-term memory recurrent neural network model returned very high values of predictive accuracy, thus reinforcing the strength and reliability of our framework.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6624-6633"},"PeriodicalIF":2.1,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0