Relevant bibliographies by topics / Bessel's equation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Bessel's equation'

Author: Grafiati
Published: 4 June 2025
Last updated: 14 July 2025

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Journal articles on the topic "Bessel's equation"

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Tran, Dung Anh, Hang Thi Chu, and Long Ta Bui. "Application of the Bessel function to compute the air pollutant with the stratification of the atmospheric." Science and Technology Development Journal 18, no. 2 (2015): 14–20. http://dx.doi.org/10.32508/stdj.v18i2.1067.

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The Bessel differential equation with the Bessel function of solution has been applied. Bessel functions are the canonical solutions of Bessel's differential equation. Bessel's equation arises when finding separable solutions to Laplace's equation in cylindrical or spherical coordinates. Bessel functions are important for many problems of advection–diffusion progress and wave propagation. In this paper, authors present the analytic solutions of the atmospheric advection-diffusion equation with the stratification of the boundary condition. The solution has been found by applied the separation o
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Mulyati, Annisa Eki, and Sugiyanto Sugiyanto. "Aplikasi Persamaan Bessel Orde Nol Pada Persamaan Panas Dua Dimensi." Jurnal Fourier 2, no. 2 (2013): 113. http://dx.doi.org/10.14421/fourier.2013.22.113-123.

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Bessel differential equation is one of the applied equation in physics is about heat transfer. Application of modified Bessel function of order zero on heat transfer process of two-dimensional objects which can be modelled in the form of a two-order partial differential equations as follows, ..... With the obtained solutions of Bessel's differential equation application of circular fin, .... two-dimensional temperature stated on the point ..... against time t
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Sudhanshu, Aggarwal. "ELZAKI TRANSFORM OF BESSEL'S FUNCTIONS." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 5, no. 8 (2018): 45–51. https://doi.org/10.5281/zenodo.1339350.

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In the modern time, Bessel’s functions appear in solving many problems of sciences and engineering together with many equations such as heat equation, wave equation, Laplace equation, Schrodinger equation, Helmholtz equation in cylindrical or spherical coordinates. In this paper, we determine Elzaki transform of Bessel’s functions. Some applications of Elzaki transform of Bessel’s functions for evaluating the integral, which contain Bessel’s functions, are given.
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HOFFMANN, CHRISTOPH. "Constant differences: Friedrich Wilhelm Bessel, the concept of the observer in early nineteenth-century practical astronomy and the history of the personal equation." British Journal for the History of Science 40, no. 3 (2007): 333–65. http://dx.doi.org/10.1017/s0007087407009478.

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AbstractIn 1823 the astronomer Friedrich Wilhelm Bessel gave notice of an observational error which is now known as the personal equation. Bessel, however, never used this phrase to characterize the finding that when noting the time of a certain event observers show a considerable ‘involuntary constant difference’. From this starting point the paper develops two arguments. First, these involuntary differences subverted the concept of the ‘observing observer’. What had previously been defined as a reference point of trust and precision turned into a source of an error that resisted any wilful i
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Kim, Byungbae, and Soon-Mo Jung. "Bessel's Differential Equation and Its Hyers-Ulam Stability." Journal of Inequalities and Applications 2007, no. 1 (2007): 021640. http://dx.doi.org/10.1155/2007/21640.

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MARTINEZ-MORALES, JOSE L. "THE SCHRÖDINGER PROPAGATOR AS A WAVE FUNCTION OF THE WHEELER–DE WITT EQUATION." Modern Physics Letters A 25, no. 15 (2010): 1289–94. http://dx.doi.org/10.1142/s0217732310032573.

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The eigenvalue equation of the dynamical Schrödinger operator in polar coordinates without potential is considered. An integral transformation in terms of the Bessel's functions is suggested as a solution. The eigenvalue equation is simplified to an ordinary equation in the time variable. The Schrödinger propagator is calculated with the solution of the eigenvalue equation, and used to find explicitly the wave function of the Wheeler–de Witt equation that describes gravity plus a perfect fluid.
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Cho, Ingoo, and Hwajoon Kim. "The solution of Bessel's equation by using integral transforms." Applied Mathematical Sciences 7 (2013): 6069–75. http://dx.doi.org/10.12988/ams.2013.39518.

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Gehlot, Kuldeep Singh. "Differential equation of K-Bessel's function and its properties." Nonlinear Analysis and Differential Equations 2 (2014): 61–67. http://dx.doi.org/10.12988/nade.2014.3821.

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Pham Ngoc Dinh, A. "Existence and uniqueness of solution of Bessel's nonlinear differential equation." Mathematical and Computer Modelling 11 (1988): 676–78. http://dx.doi.org/10.1016/0895-7177(88)90578-x.

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Nguyen Thanh Long and Alain Pham Ngoc Dinh. "Periodic solution of a nonlinear parabolic equation involving Bessel's operator." Computers & Mathematics with Applications 25, no. 5 (1993): 11–18. http://dx.doi.org/10.1016/0898-1221(93)90194-z.

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Dissertations / Theses on the topic "Bessel's equation"

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Witenberg, Anna. "Zastosowanie wybranej klasy wielomianów do zapewnienia stabilności późnoczasowego rozwiązania równań EFIE modelujących anteny liniowe." Rozprawa doktorska, Uniwersytet Technologiczno-Przyrodniczy w Bydgoszczy, 2015. http://dlibra.utp.edu.pl/Content/818.

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W pracy zaproponowano metodę hybrydową polegającą na mieszanym numeryczno-analitycznym opisie procesu ograniczenia lub uniknięcia utraty stabilności obliczeń późnoczasowego rozwiązania całkowych równań pola elektrycznego modelujących anteny liniowe w dziedzinie czasu. Pokazano zastosowanie w metodzie hybrydowej wybranych funkcji, głównie wielomianów pozwalających na uproszczenie procesu aproksymacji w części analitycznej
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Takata, Tomohiro. "Certain multiple orthogonal polynomials and a discretization of the Bessel equation." 京都大学 (Kyoto University), 2006. http://hdl.handle.net/2433/144354.

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Kyoto University (京都大学)<br>0048<br>新制・課程博士<br>博士(理学)<br>甲第11975号<br>理博第2955号<br>新制||理||1442(附属図書館)<br>23788<br>UT51-2006-C655<br>京都大学大学院理学研究科数学・数理解析専攻<br>(主査)教授 上野 健爾, 教授 井川 満, 教授 河野 明<br>学位規則第4条第1項該当
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Coelho, João Bosco. "Corda vibrante e telegrafo : estudo analitico de problemas modelados por equações diferenciais." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307008.

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Orientador: Edmundo Capelas de Oliveira<br>Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-11T05:13:17Z (GMT). No. of bitstreams: 1 Coelho_JoaoBosco_M.pdf: 1003588 bytes, checksum: c8b5b0bbc0f7fe49adbeacc39f398bcf (MD5) Previous issue date: 2008<br>Resumo: Efetua-se um estudo sistemático das equações diferenciais parciais, lineares, de segunda ordem e do tipo hiperbólico, isto é, aquelas equações que estão associadas com o problema envolvendo a propagação de ondas. Com
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Rodrigues, Fabio Grangeiro 1980. "Sobre cálculo fracionário e soluções da equação de Bessel." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306992.

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Orientador: Edmundo Capelas de Oliveira<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-26T23:00:41Z (GMT). No. of bitstreams: 1 Rodrigues_FabioGrangeiro_D.pdf: 1185818 bytes, checksum: 96f82c6ff4622e4ecdd3ccae79803dae (MD5) Previous issue date: 2015<br>Resumo: Neste trabalho é apresentado um modo de se obter soluções de um caso particular da equação hipergeométrica confluente, a equação de Bessel de ordem p, utilizando-se da teoria do cálculo de ordem arbitrária, também conhecido pop
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Chellali, Mustapha. "Congruences, nombres de Bernoulli et polynômes de Bessel." Université Joseph Fourier (Grenoble ; 1971-2015), 1989. http://www.theses.fr/1989GRE10091.

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En premiere partie, on donne des congruences entre nombres de bernoulli-hcowitz dans le cas supersingulier. En deuxieme partie, on montre que la suite des nombres de bernoulli verifie des formules de recurrence qui servent a tester si un nombre premier est irregulier. En troisieme partie, on etudie les zeros des polynomes de bessel generalises, en particulier on encadre un zero reel, apres developpement asymptotique, et on donne des estimations uniformes des valeurs de ces polynomes
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Zhelezov, Gleb, and Gleb Zhelezov. "Coalescing Particle Systems and Applications to Nonlinear Fokker-Planck Equations." Diss., The University of Arizona, 2017. http://hdl.handle.net/10150/624562.

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We study a stochastic particle system with a logarithmically-singular inter-particle interaction potential which allows for inelastic particle collisions. We relate the squared Bessel process to the evolution of localized clusters of particles, and develop a numerical method capable of detecting collisions of many point particles without the use of pairwise computations, or very refined adaptive timestepping. We show that when the system is in an appropriate parameter regime, the hydrodynamic limit of the empirical mass density of the system is a solution to a nonlinear Fokker-Planck equation,
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Chen, Huyuan. "Fully linear elliptic equations and semilinear fractionnal elliptic equations." Thesis, Tours, 2014. http://www.theses.fr/2014TOUR4001/document.

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Cette thèse est divisée en six parties. La première partie est consacrée à l'étude de propriétés de Hadamard et à l'obtention de théorèmes de Liouville pour des solutions de viscosité d'équations aux dérivées partielles elliptiques complètement non-linéaires avec des termes de gradient,<br>This thesis is divided into six parts. The first part is devoted to prove Hadamard properties and Liouville type theorems for viscosity solutions of fully nonlinear elliptic partial differential equations with gradient term
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Polat, Zeynep Sonay. "Studies On The Generalized And Reverse Generalized Bessel Polynomials." Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12604961/index.pdf.

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The special functions and, particularly, the classical orthogonal polynomials encountered in many branches of applied mathematics and mathematical physics satisfy a second order differential equation, which is known as the equation of the hypergeometric type. The variable coefficients in this equation of the hypergeometric type are of special structures. Depending on the coefficients the classical orthogonal polynomials associated with the names Jacobi, Laguerre and Hermite can be derived as solutions of this equation. In this thesis, these well known classical polynomials as well as another
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Zhang, Lei, University of Western Sydney, of Science Technology and Environment College, and School of Engineering and Industrial Design. "Exact solution for vibration of stepped circular Mindlin plates." THESIS_CSTE_EID_Zhang_L.xml, 2002. http://handle.uws.edu.au:8081/1959.7/64.

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This thesis presents the first-known exact solutions for vibration of stepped circular Mindlin plates. The considered circular plate is of several step-wise variation in thickness in the radial direction. The Mindlin first order shear deformable plate theory is employed to derive the governing differential equations for the annular and circular segments. The exact solutions to these differential equations may be expressed in terms of the Bessel functions of the first and second kinds and the modified Bessel functions of the first and second kinds. The governing homogenous system of equations i
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GOFFI, ALESSANDRO. "Topics in nonlinear PDEs: from Mean Field Games to problems modeled on Hörmander vector fields." Doctoral thesis, Gran Sasso Science Institute, 2019. http://hdl.handle.net/20.500.12571/9808.

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This thesis focuses on qualitative and quantitative aspects of some nonlinear PDEs arising in optimal control and differential games, ranging from regularity issues to maximum principles. More precisely, it is concerned with the analysis of some fully nonlinear second order degenerate PDEs over Hörmander vector fields that can be written in Hamilton-Jacobi-Bellman and Isaacs form and those arising in the recent theory of Mean Field Games, where the prototype model is described by a coupled system of PDEs involving a backward Hamilton-Jacobi and a forward Fokker-Planck equation. The thesis is d
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Books on the topic "Bessel's equation"

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Mann, Peter. Wave Mechanics & Elements of Mathematical Physics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0005.

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This chapter presents an in-depth look at classical wave mechanics and mathematical physics, containing key examples directly relevant to molecular physics. The separation of variables is used to construct the Helmholtz equation from the one-dimensional wave equation before considering the three-dimensional wave equation. From this, equations for the temporal, radial, azimuth and angular components are developed and solutions using the Bessel equations and Legendre polynomials are found. Boundary conditions are explained and the Rayleigh plane wave expansion as the general solution to the Helm
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Book chapters on the topic "Bessel's equation"

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Wong, M. W. "The Bessel Potential." In Partial Differential Equations, 2nd ed. Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003206781-9.

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Rodrigues, M. M., N. Vieira, and S. Yakubovich. "Operational Calculus for Bessel’s Fractional Equation." In Advances in Harmonic Analysis and Operator Theory. Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0516-2_20.

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Wong, M. W. "The Bessel–Poisson Kernel." In Partial Differential Equations, 2nd ed. Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003206781-12.

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Zhu, Yichao. "Bessel Functions." In Equations and Analytical Tools in Mathematical Physics. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-5441-1_5.

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Zhu, Yichao. "Bessel Functions." In Equations and Analytical Tools in Mathematical Physics. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-5441-1_5.

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Saxena, Vinod Prakash, Praveen Agarwal, and Altaf Ahmad Bhat. "Integral Equations Involving Bessel–Maitland Functions." In I-Function and Its Applications. Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781003517757-6.

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Mandal, B. N., and Nanigopal Mandal. "Dual integral equations with Bessel function kernel." In Advances in dual integral equations. Routledge, 2022. http://dx.doi.org/10.1201/9781315136851-2.

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Costa, Peter J. "Fourier Series, Bessel Functions, and Mathematical Physics." In Select Ideas in Partial Differential Equations. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-031-02434-4_4.

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Mota, Eduardo. "Constant Mean Curvature Surfaces for the Bessel Equation." In Minimal Surfaces: Integrable Systems and Visualisation. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-68541-6_12.

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Floreanini, Roberto, and Luc Vinet. "Basic Bessel functions and 𝑞-difference equations." In CRM Proceedings and Lecture Notes. American Mathematical Society, 1996. http://dx.doi.org/10.1090/crmp/009/11.

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Conference papers on the topic "Bessel's equation"

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Rahimov, F. "Use of Eigenvalue Stability Analysis for Liner Inflow Test Interpretation." In SPE Advances in Integrated Reservoir Modelling and Field Development Conference and Exhibition. SPE, 2025. https://doi.org/10.2118/225392-ms.

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Summary The Well Integrity Management System is a central policy outlining well integrity requirements to ensure operational safety and safe production throughout well lifecycle. Among these requirements is a liner inflow test, particularly when set above the production packer to prevent any potential non-conformities such as Sustained Casing Pressure, tubular corrosion, an underground blowout and many other Well Integrity issues during production. Some Well Integrity Guidelines propose the use of Horner's technique to interpret these tests where predictions are made based on the Y-intercept o
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Loganathan, S., S. Sarala, A. Balasubramanian, and M. Radha Madhavi. "Machine learning approach to solve Bessel’s equation." In ESSENCE OF MATHEMATICS IN ENGINEERING APPLICATIONS: EMEA-2020. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0066945.

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Loganathan, S., S. Sarala, A. Balasubramanian, and M. Radha Madhavi. "Machine learning approach to solve Bessel’s equation." In ESSENCE OF MATHEMATICS IN ENGINEERING APPLICATIONS: EMEA-2020. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0066945.

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Campo, Antonio. "Approximate Temperature Profiles and Companion Heat Transfer Rates of Uniform Annular Fins Using Finite-Differences Instead of Bessel Functions." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-1144.

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Abstract The temperature variation along annular fins of uniform thickness and constant thermal conductivity is governed by a differential equation of second order with variable coefficients which is called the modified Bessel equation of zero order. This educational paper addresses a simplistic finite-difference procedure for solving this kind of Bessel equation employing a reduced system of algebraic equations. Approximate temperature distributions and companion heat transfer rates have been computed with the elimination of unknowns by hand and also with the Gauss elimination method using th
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Jabbari, Mohsen, Amir Hossein Mohazzab, and Ali Bahtui. "One Dimensional Moving Heat Source in Hollow FGM Cylinder." In ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/pvp2006-icpvt-11-93145.

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This paper presents the analytical solution of one-dimensional mechanical and thermal stresses for a hollow cylinder made of functionally graded material. The material properties vary continuously across the thickness, according to power functions of radial direction. Temperature distribution is symmetric, and transient. The thermal boundary conditions may include conduction, flux, and convection for inside or outside of hollow cylinder. Thermoelasticity equation is transient, including the moving heat source. The heat conduction and Navier equations are solved analytically, using the generali
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Venkataraman, P. "Solving Inverse ODE Using Bezier Functions." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86331.

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The simplest inverse boundary value problem is to identify the differential equation and the boundary conditions from a given set of discrete data points. For an ordinary differential equation, it would involve finding a function, which when expressed through some function of itself and its derivatives, and integrated using particular boundary conditions would generate the given data. Parametric Bezier functions are excellent candidates for these functions. They allow efficient approximation of data and its derivative content. The Bezier function is smooth and continuous to a high degree. In t
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Sharma, Kal Renganathan. "On Relativistic Transformation of Coordinates and Exact Solution of Damped Wave Conduction and Relaxation Equation." In ASME 2008 Heat Transfer Summer Conference collocated with the Fluids Engineering, Energy Sustainability, and 3rd Energy Nanotechnology Conferences. ASMEDC, 2008. http://dx.doi.org/10.1115/ht2008-56121.

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Analytical solution to the hyperbolic damped wave conduction and relaxation equation is developed by a novel method called the relativistic transformation method. The hyperbolic PDE is decomposed into a time decaying damping component and a Klein-Gardon type equation for the wave temperature. The PDE that describes the wave temperature is transformed to a Bessel differential equation by using the relativistic transformation. The relativistic transformation, η = τ2 − X2 is symmetric in space and time. The solution obtained for the transient temperature to a semi-infinite medium was compared wit
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RAPPOPORT, JURI M. "SOME INTEGRAL EQUATIONS WITH MODIFIED BESSEL FUNCTIONS." In Proceedings of the 5th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812835635_0025.

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Debeerst, Ruben, Mark van Hoeij, and Wolfram Koepf. "Solving differential equations in terms of bessel functions." In the twenty-first international symposium. ACM Press, 2008. http://dx.doi.org/10.1145/1390768.1390777.

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Weiss, George. "Approximated Fundamental Frequency for Thin Circular Plates Clamped or Pinned at the Edge." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-41018.

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Calculating the exact solution to the differential equations that describe the motion of a circular plate clamped or pinned at the edge, is laborious. The calculations include the Bessel functions and modified Bessel functions. In this paper, we present a brief method for calculating with approximation, the fundamental frequency of a circular plate clamped or pinned at the edge. We’ll use the Dunkerley’s estimate to determine the fundamental frequency of the plates. A plate is a continuous system and will assume it is loaded with a uniform distributed load, including the weight of the plate it
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