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Journal articles on the topic 'Bessel's equation'

Author: Grafiati

Published: 4 June 2025

Last updated: 14 July 2025

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Wu, Di, and Bao Sheng Zhao. "A Refined Theory of Axisymmetric Thermoelastic Circular Cylinder with Transversely Isotropic." Advanced Materials Research 622-623 (December 2012): 1611–15. http://dx.doi.org/10.4028/www.scientific.net/amr.622-623.1611.

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For analyzing the exact stress field, the exact displacement field and the exact temperature field in axisymmetric thermoelastic circular cylinder with transversely isotropic, the refined theory of an axisymmetric circular cylinder was researched. Without ad hoc assumptions, the refined equation of an axisymmetric thermoelastic circular cylinder with transversely isotropic was obtained, which yields Bessel's function and the solution of the cylinder directly from the general solution. By dropping terms of high order, the approximate solutions are derived for a circular cylinder under radial di

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12

DENG, YINBIN, and YI LI. "EXPONENTIAL DECAY OF THE SOLUTIONS FOR NONLINEAR BIHARMONIC EQUATIONS." Communications in Contemporary Mathematics 09, no. 05 (2007): 753–68. http://dx.doi.org/10.1142/s0219199707002629.

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The purpose of this paper is to establish the exponential decay properties of the solutions for the nonlinear biharmonic equation [Formula: see text] We introduce the fundamental solutions for the linear biharmonic operator Δ2 - λ if λ < 0. By applying some properties of Hankel functions, which are the solutions of Bessel's equation, we obtain the asymptotic representation of the fundamental solution of Δ2 - λ at ∞ and 0. Asymptotic estimates of the solutions of (*) can be obtained from the properties of the fundamental solutions of Δ2 - λ.

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13

Yürekli, Osman, and Scott Wilson. "A new method of solving Bessel's differential equation using the -transform." Applied Mathematics and Computation 130, no. 2-3 (2002): 587–91. http://dx.doi.org/10.1016/s0096-3003(01)00119-9.

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14

Thi Thanh Binh, D., A. Pham Ngoc Dinh, and N. Thanh Long. "Linear recursive schemes associated with the nonlinear wave equation involving Bessel's operator." Mathematical and Computer Modelling 34, no. 5-6 (2001): 541–56. http://dx.doi.org/10.1016/s0895-7177(01)00082-6.

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15

Long, Nguyen Thanh, and Alain Pham Ngoc Dinh. "On a nonlinear parabolic equation involving Bessel's operator associated with a mixed inhomogeneous condition." Journal of Computational and Applied Mathematics 196, no. 1 (2006): 267–84. http://dx.doi.org/10.1016/j.cam.2005.07.024.

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16

Singh, A. K., Z. Parween, A. Das, and A. Chattopadhyay. "Influence of Loosely-Bonded Sandwiched Initially Stressed Visco-Elastic Layer on Torsional Wave Propagation." Journal of Mechanics 33, no. 3 (2016): 351–68. http://dx.doi.org/10.1017/jmech.2016.107.

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AbstractAssumption that the common interfaces of the media are perfectly bonded may not be always true. Situation may arise that composition of the two medium may be responsible for weakening the contact between them. So, it becomes obligatory to consider a loosely bonded interface in such cases which may affect the propagation of elastic waves through them. This paper thrashes out the propagation of torsional surface wave in an initially stressed visco-elastic layer sandwiched between upper and lower initially stressed dry-sandy Gibson half-spaces, theoretically. Both the upper and lower dry-

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17

Reuster, D., and M. Kaye. "A technique for developing complete orthonormal basis sets using general solutions of Bessel's differential equation." Applied Mathematics and Computation 55, no. 2-3 (1993): 255–64. http://dx.doi.org/10.1016/0096-3003(93)90024-9.

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18

MARETIC, RATKO, and VALENTIN GLAVARDANOV. "VIBRATION OF CIRCULAR PLATE WITH AN INTERNAL ELASTIC RING SUPPORT UNDER EXTERIOR EDGE PRESSURE." International Journal of Structural Stability and Dynamics 14, no. 01 (2013): 1350053. http://dx.doi.org/10.1142/s0219455413500533.

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In this paper, we analyze the transverse vibration of a circular plate loaded by uniform pressure along its edge. The plate is supported by an elastic ring support being coaxial with the plate. At its edge the plate is clamped but the radial displacement is allowed. Apart from this problem, the heated plate clamped at its edge, but without the possibility of radial displacement, is also analyzed. The analytical solution of governing equation is obtained in the form of Bessel's functions. Using the analytical solution, the frequencies of transverse vibrations depending on loads, elastic ring st

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Minchenko, Andrei, and Alexey Ovchinnikov. "Calculating Galois groups of third-order linear differential equations with parameters." Communications in Contemporary Mathematics 20, no. 04 (2018): 1750038. http://dx.doi.org/10.1142/s0219199717500389.

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Motivated by developing algorithms that decide hypertranscendence of solutions of extensions of the Bessel differential equation, algorithms computing the unipotent radical of a parameterized differential Galois group have been recently developed. Extensions of Bessel’s equation, such as the Lommel equation, can be viewed as homogeneous parameterized linear differential equations of the third order. In this paper, we give the first known algorithm that calculates the differential Galois group of a third-order parameterized linear differential equation.

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20

SN, Maitra. "Motion of A Rocket in Three-Dimension with Constant Thrust Over A Spherical Rotating Earth Holding Constant Heading and Constant Path Inclination." International Journal of Engineering Research & Science 5, no. 5 (2019): 12–14. https://doi.org/10.5281/zenodo.3256285.

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<strong><em>Abstract</em></strong><strong>—</strong> <em>In this paper we have determined the velocity and altitude of a spacecraft and then equation of its trajectory with constant thrust, constant heading and constant path-inclination by regulating the bank angle and angle of attack.</em>

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21

van der Toorn, Ramses. "Tandem Recurrence Relations for Coefficients of Logarithmic Frobenius Series Solutions about Regular Singular Points." Axioms 12, no. 1 (2022): 32. http://dx.doi.org/10.3390/axioms12010032.

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We enhance Frobenius’ method for solving linear ordinary differential equations about regular singular points. Key to Frobenius’ approach is the exploration of the derivative with respect to a single parameter; this parameter is introduced through the powers of generalized power series. Extending this approach, we discover that tandem recurrence relations can be derived. These relations render coefficients for series occurring in logarithmic solutions. The method applies to the, practically important, exceptional cases in which the roots of the indicial equation are equal, or differ by a non-z

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22

Sharma, Sonia, and Harish Nagar. "Complex Sadik integral transform of Bessel’s function of first kind." Journal of Interdisciplinary Mathematics 28, no. 4 (2025): 1695–701. https://doi.org/10.47974/jim-2267.

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The Laplace equation, the heat equation, the wave equation, and the Helmholtz equation in cylindrical or spherical coordinates are just a few of the numerous equations that may be solved using Bessel’s functions in modern engineering and natural science applications. In this paper, we present some important applications for assessing the integration as well as the intricate Sadik integral transform of Bessel’s functions. The efficiency of the complex Sadik integral transform and its ability to provide an accurate solution with the fewest number of calculations are demonstrated using real-world

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23

Yilmazer, Resat, and Okkes Ozturk. "On nabla discrete fractional calculus operator for a modified Bessel equation." Thermal Science 22, Suppl. 1 (2018): 203–9. http://dx.doi.org/10.2298/tsci170614287y.

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In thermal sciences, it is possible to encounter topics such as Bessel beams, Bessel functions or Bessel equations. In this work, we also present new discrete fractional solutions of the modified Bessel differential equation by means of the nabla-discrete fractional calculus operator. We consider homogeneous and non-homogeneous modified Bessel differential equation. So, we acquire four new solutions of these equations in the discrete fractional forms via a newly developed method

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24

Pandey, C. P., P. Phukan, and K. Moungkang. "SOLUTION OF INTEGRAL EQUATIONS BY BESSEL WAVELET TRANSFORM." Advances in Mathematics: Scientific Journal 10, no. 4 (2021): 2245–53. http://dx.doi.org/10.37418/amsj.10.4.38.

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The integral equations of the first kind arise in many areas of science and engineering fields such as image processing and electromagnetic theory. The wavelet transform technique to solve integral equation allows the creation of very fast algorithms when compared with known algorithms. Various wavelet methods are used to solve certain type of integral equations. To find the most accurate and stable solution of the integral equation Bessel wavelet is the appropriate method. To study the properties of solution of integral equations on distribution spaces Bessel wavelet transform is also used. I

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25

Sudhanshu Aggarwal, Anuj Kumar, and Shikha Bansal. "Bessel functions of first kind and their Anuj transforms." World Journal of Advanced Research and Reviews 19, no. 1 (2023): 672–81. http://dx.doi.org/10.30574/wjarr.2023.19.1.1381.

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Various problems of Statistics, Mathematics, Radio Physics, Nuclear Physics, Atomic Physics, Fluid Mechanics, Engineering and Science can easily handle by applying integral transform techniques on their mathematical models. Problems of heat equation, Schrodinger equation, Laplace equation, Helmholtz equation and wave equation have solutions in terms of Bessel functions. To solve such equations by integral transform methods, we need to know the integral transform of Bessel functions. In this paper, authors discuss Bessel functions of first kind and determine their Anuj transforms.

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Sudhanshu, Aggarwal, Kumar Anuj, and Bansal Shikha. "Bessel functions of first kind and their Anuj transforms." World Journal of Advanced Research and Reviews 19, no. 1 (2023): 672–81. https://doi.org/10.5281/zenodo.10254641.

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Various problems of Statistics, Mathematics, Radio Physics, Nuclear Physics, Atomic Physics, Fluid Mechanics, Engineering and Science can easily handle by applying integral transform techniques on their mathematical models. Problems of heat equation, Schrodinger equation, Laplace equation, Helmholtz equation and wave equation have solutions in terms of Bessel functions. To solve such equations by integral transform methods, we need to know the integral transform of Bessel functions. In this paper, authors discuss Bessel functions of first kind and determine their Anuj transforms.

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27

Mehdi, Sadiq A., Emad A. Kuffi, and Jinan A. Jasim. "SEJI integral transform of Bessel’s functions." Journal of Interdisciplinary Mathematics 26, no. 6 (2023): 1159–69. http://dx.doi.org/10.47974/jim-1614.

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Bessel’s functions have great mathematical importance in solving differential equations, especially in the applied field. There is a lot of research that review some applied equations and their solutions using these functions. Since integral transforms have high efficiency in finding accurate solutions to distinct kinds of differential and integral equations, we use in this paper the proposed method “SEJI integral transform” for functions of Bessel. These certain applications have been taken for these functions and solved by SEJI integral transform that reached to the exact solutions. In addit

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28

Derle, Monali, and Dinkar Patil. "Applications of The Double General Rangaig Integral Transform in Integro-Differential Equations." Indian Journal Of Science And Technology 17, no. 31 (2024): 3258–71. http://dx.doi.org/10.17485/ijst/v17i31.922.

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Objectives : To solve integral differential equations. Method: The convolution theory and double general Rangaig integral transform was used to solve integral differential equations, precisely. Findings: The present study derives the existence condition of the double general Rangaig integral transform. Theorems proved in this study, deals with popular properties of the double general Rangaig integral transform. The double general Rangaig integral transform of Bessel's function and modified Bessel's function are calculated. The convolution theorem has been stated and demonstrated using the unit

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Castro, L. P., and A. M. Simões. "A Hyers-Ulam stability analysis for classes of Bessel equations." Filomat 35, no. 13 (2021): 4391–403. http://dx.doi.org/10.2298/fil2113391c.

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Mathematical modeling helps us to better understand different natural phenomena. Modeling is most of the times based on the consideration of appropriate equations (or systems of equations). Here, differential equations are well-known to be very useful instruments when building mathematical models - specially because that the use of derivatives offers several interpretations associated with real life laws. Differential equations are classified based on several characteristics and, in this way, allow different possibilities of building models. In this paper we will be concentrated in analysing c

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MOMONIAT, E. "A COMPARISON OF DIFFUSION MODELED BY TWO MIXED DERIVATIVE EQUATIONS." Modern Physics Letters B 22, no. 27 (2008): 2709–13. http://dx.doi.org/10.1142/s0217984908017254.

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Fourier and Bessel function solutions of two mixed derivative equations are investigated. For the appropriate sign of the material constants in the derivation of the mixed derivative equation, we obtain both Fourier and Bessel function solutions that tend to the corresponding solutions of the phenomenological diffusion equation. For the opposite sign of the material constants, the solutions diverge.

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Mandal, B. N. "A note on Bessel function dual integral equation with weight function." International Journal of Mathematics and Mathematical Sciences 11, no. 3 (1988): 543–49. http://dx.doi.org/10.1155/s0161171288000651.

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An elementary procedure based on Sonine's integrals has been used to reduce dual integral equations with Bessel functions of different orders as kernels and an arbitrary weight function to a Fredholm integral equation of the second kind. The result obtained here encompasses many results concerning dual integral equations with Bessel functions as kernels known in the literature.

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Melnychuk, L. "FUNDAMENTAL SOLUTION OF THE CAUCHY PROBLEM FOR PARABOLIC EQUATION OF THE SECOND ORDER WITH INCREASING COEFFICIENTS AND WITH BESSEL OPERATORS OF DIFFERENT ORDERS." Bukovinian Mathematical Journal 10, no. 2 (2022): 176–84. http://dx.doi.org/10.31861/bmj2022.02.13.

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The theory of the Cauchy problem for uniformly parabolic equations of the second order with limited coefficients is sufficiently fully investigated, for example, in the works of S.D. Eidelman and S.D. Ivasyshen, in contrast to such equations with unlimited coefficients. One of the areas of research of Professor S.D. Ivasyshen and students of his scientific school are finding fundamental solutions and investigating the correctness of the Cauchy problem for classes of degenerate equations, which are generalizations of the classical Kolmogorov equation of diffusion with inertia and contain for th

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33

Campos, L. M. B. C., and M. J. S. Silva. "On Generalised Hankel Functions and a Bifurcation of Their Asymptotic Expansion." WSEAS TRANSACTIONS ON MATHEMATICS 23 (April 10, 2024): 237–52. http://dx.doi.org/10.37394/23206.2024.23.26.

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The generalised Bessel differential equation has an extra parameter relative to the original Bessel equation and its asymptotic solutions are the generalised Hankel functions of two kinds distinct from the original Hankel functions. The generalised Bessel differential equation of order ν and degree μ reduces to the original Bessel differential equation of order ν for zero degree, μ = 0. In both cases the differential equations have a regular singularity near the origin and the the point at infinity is the other singularity. The point at infinity is an irregular singularity of different degree,

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34

Karimov, Shakhobiddin, and Yorkinoy Tulasheva. "Solution of an Initial Boundary Value Problem for a Multidimensional Fourth-Order Equation Containing the Bessel Operator." Mathematics 12, no. 16 (2024): 2503. http://dx.doi.org/10.3390/math12162503.

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In the present work, the transmutation operator approach is employed to construct an exact solution to the initial boundary-value problem for multidimensional free transverse equation vibration of a thin elastic plate with a singular Bessel operator acting on geometric variables. We emphasize that multidimensional Erdélyi–Kober operators of a fractional order have the property of a transmutation operator, allowing one to transform more complex multidimensional partial differential equations with singular coefficients acting over all variables into simpler ones. If th formulas for solutions are

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35

Ivashkevich, A. V., E. M. Ovsiyuk, V. V. Kisel, and V. M. Red’kov. "Spherical solutions of the wave equation for a spin 3/2 particle." Doklady of the National Academy of Sciences of Belarus 63, no. 3 (2019): 282–90. http://dx.doi.org/10.29235/1561-8323-2019-63-3-282-290.

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The wave equation for a spin 3/2 particle, described by 16-component vector-bispinor, is investigated in spherical coordinates. In the frame of the Pauli–Fierz approach, the complete equation is split into the main equation and two additional constraints, algebraic and differential. The solutions are constructed, on which 4 operators are diagonalized: energy, square and third projection of the total angular momentum, and spatial reflection, these correspond to quantum numbers {ε, j, m, P}. After separating the variables, we have derived the radial system of 8 first-order equations and 4 additi

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36

Monali, Derle, and Patil Dinkar. "Applications of The Double General Rangaig Integral Transform in Integro-Differential Equations." Indian Journal of Science and Technology 17, no. 31 (2024): 3258–71. https://doi.org/10.17485/IJST/v17i31.922.

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Abstract <strong>Objectives :</strong> To solve integral differential equations. <strong>Method:</strong> The convolution theory and double general Rangaig integral transform was used to solve integral differential equations, precisely. <strong>Findings:</strong> The present study derives the existence condition of the double general Rangaig integral transform. Theorems proved in this study, deals with popular properties of the double general Rangaig integral transform. The double general Rangaig integral transform of Bessel's function and modified Bessel's function ar

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37

Khudoynazarov, Khayrulla. "A mathematical model of physically nonlinear torsional vibrations of a circular elastic rod." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 84 (2023): 152–66. https://doi.org/10.17223/19988621/84/12.

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A mathematical model of non-stationary torsional vibrations of a circular elastic rod is developed taking into account the Kauderer nonlinear law of elasticity. To solve this problem, the nonlinear equation of motion of an elastic body with torsional vibrations of a rod is reduced to two linear Bessel equations (homogeneous and inhomogeneous) in transformations. Considering general solutions of the obtained equations with zero initial and given boundary conditions on the surface of the rod, a refined physically nonlinear equation of torsional vibrations of the rod made of homogeneous and isotr

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38

Ibragimova, Nailya. "Construction of a fundamental solution for a one degenerating elliptic equation with a Bessel operator." Tambov University Reports. Series: Natural and Technical Sciences, no. 125 (2019): 47–59. http://dx.doi.org/10.20310/1810-0198-2019-24-125-47-59.

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Degenerating elliptic equations containing the Bessel operator are mathematical models of axial and multi-axial symmetry of a wide variety of processes and phenomena of the surrounding world. Difficulties in the study of such equations are associated, inter alia, with the presence of singularities in the coefficients. This article considers a p -dimensional, p≥3 ; degenerating elliptic equation with a negative parameter, in which the Bessel operator acts on one of the variables. A fundamental solution of this equation is constructed and its properties are investigated, in particular, the behav

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Krahmaleva, Yu R. "Bessel equation and functions in computer mathematics system." Mechanics and Technologies, no. 2 (June 30, 2024): 426–39. https://doi.org/10.55956/rzbk3395.

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The relevance of technical issues of solving problems of mathematical physics is growing every year. The development of computer technologies leads to the use of modern methods for their solution. The application of analytical computing systems is considered as an effective method, which contributes to their productive implementation. The article deals with finding a general solution of the Bessel equation and equations leading to it in the Maple program, graphs of functions are plotted

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40

Diouf, Edouard. "Analytical Solution of the Schrödinger Equation with an Exponential Type Mass Depending on the Spatial Variable." European Journal of Theoretical and Applied Sciences 1, no. 4 (2023): 712–17. http://dx.doi.org/10.59324/ejtas.2023.1(4).65.

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In the present work, we proceed to study the Schrödinger equation with dependent mass position. From the resulting partial differential equations, we obtain exact analytical solutions governed by Bessel functions. The exact solution of Schrödinger's equation for a particle with dependent position of the mass (PDM) is a "half-harmonic potential" defined in a Hilbert space. The harmonic oscillator is carried by the wave function ψ(x) through the Bessel function. The magnitude of ψ(x) increases dramatically as the values of the spatial coordinate become larger and larger. This growth is all the m

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41

Izadi, Mohammad, Şuayip Yüzbaşi, and Samad Noeiaghdam. "Approximating Solutions of Non-Linear Troesch’s Problem via an Efficient Quasi-Linearization Bessel Approach." Mathematics 9, no. 16 (2021): 1841. http://dx.doi.org/10.3390/math9161841.

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Two collocation-based methods utilizing the novel Bessel polynomials (with positive coefficients) are developed for solving the non-linear Troesch’s problem. In the first approach, by expressing the unknown solution and its second derivative in terms of the Bessel matrix form along with some collocation points, the governing equation transforms into a non-linear algebraic matrix equation. In the second approach, the technique of quasi-linearization is first employed to linearize the model problem and, then, the first collocation method is applied to the sequence of linearized equations iterati

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42

Imran, M., D. L. C. Ching, Rabia Safdar, Ilyas Khan, M. Imran, and K. Nisar. "The Solutions of Non-Integer Order Burgers’ Fluid Flowing through a Round Channel with Semi Analytical Technique." Symmetry 11, no. 8 (2019): 962. http://dx.doi.org/10.3390/sym11080962.

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The solutions for velocity and stress are derived by using the methods of Laplace transformation and Modified Bessel’s equation for the rotational flow of Burgers’ fluid flowing through an unbounded round channel. Initially, supposed that the fluid is not moving with t = 0 and afterward fluid flow is because of the circular motion of the around channel with velocity Ω R t p with time positively grater than zero. At the point of complicated expressions of results, the inverse Laplace transform is alternately calculated by “Stehfest’s algorithm” and “MATHCAD” numerically. The numerically obtaine

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Al-Musalhi, Fatma, Nasser Al-Salti, and Erkinjon Karimov. "Initial boundary value problems for a fractional differential equation with hyper-Bessel operator." Fractional Calculus and Applied Analysis 21, no. 1 (2018): 200–219. http://dx.doi.org/10.1515/fca-2018-0013.

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AbstractDirect and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart of a hyper-Bessel differential operator are considered. Solutions to these problems are constructed based on appropriate eigenfunction expansions and results on existence and uniqueness are established. To solve the resultant equations, a solution to such kind of non-homogeneous fractional differential equation is also presented.

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Edouard, Diouf. "Analytical Solution of the Schrödinger Equation with an Exponential Type Mass Depending on the Spatial Variable." European Jornal of Theoretical and Sciences 1, no. 4 (2023): 712–17. https://doi.org/10.59324/ejtas.2023.1(4).65.

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In the present work, we proceed to study the Schrödinger equation with dependent mass position. From the resulting partial differential equations, we obtain exact analytical solutions governed by Bessel functions. The exact solution of Schrödinger's equation for a particle with dependent position of the mass (PDM) is a "half-harmonic potential" defined in a Hilbert space. The harmonic oscillator is carried by the wave function ψ(x) through the Bessel function. The magnitude of ψ(x) increases dramatically as the values of the spatial coordinate become larger and

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Funes, Jorge Olivares, Elvis Valero Kari, and Pablo Martin. "The Bessel function J ₀ in fractional differential equations." Journal of Physics: Conference Series 2090, no. 1 (2021): 012093. http://dx.doi.org/10.1088/1742-6596/2090/1/012093.

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Abstract Spherical Bessel functions have many important applications in engineering, optic and science. In this work, wich is a continuation of the error function in fractional differential equations, it is shown how solve the fractional differential equation d α y d x α = j 0 ( x ) , y ( k ) ( 0 ) = 0 , k = 0 , … m − 1 , with m − 1 < α ≤ m , m ∈ Ν , where the nonhomogenous part is the function Bessel spherical J 0(x).

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Zhang, Kangqun. "Applications of Erdélyi-Kober fractional integral for solving time-fractional Tricomi-Keldysh type equation." Fractional Calculus and Applied Analysis 23, no. 5 (2020): 1381–400. http://dx.doi.org/10.1515/fca-2020-0068.

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Abstract In this paper we consider Cauchy problem of time-fractional Tricomi-Keldysh type equation. Based on the theory of a Erdélyi-Kober fractional integral operator, the formal solution of the inhomogeneous differential equation involving hyper-Bessel operator is presented with Mittag-Leffler function, then nonlinear equations are considered by applying Gronwall-type inequalities. At last, we establish the existence and uniqueness of L p -solution of time-fractional Tricomi-Keldysh type equation by use of Mikhlin multiplier theorem.

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Parand, Kourosh, and Mehran Nikarya. "Application of Bessel functions and Jacobian free Newton method to solve time-fractional Burger equation." Nonlinear Engineering 8, no. 1 (2019): 688–94. http://dx.doi.org/10.1515/nleng-2018-0128.

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Abstract In this paper, a novel method based on Bessel functions (BF), generalized Bessel functions (GBF), the collocation method and the Jacobian free Newton-Krylov sub-space (JFNK) will be introduced to solve the nonlinear time-fractional Burger equation. In this paper, an implicit formula is introduced to calculate Riemann–Liouville fractional derivative of GBFs, that can be very useful in spectral methods. In this work, the nonlinear time-fractional Burger equation is converted to a nonlinear system of algebraic equations via collocation algorithm based on BFs and GBFs without any lineariz

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Bosakov, S. V. "Two Contact Problems for Annular Rigid Stamp on an Elastic Half Space." Science & Technique 17, no. 6 (2018): 458–64. http://dx.doi.org/10.21122/2227-1031-2018-17-6-458-464.

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The paper presents solutions of two contact problems for the annular plate die on an elastic half-space under the action of axisymmetrically applied force and moment. Such problems usually arise in the calculation of rigid foundations with the sole of the annular shape in chimneys, cooling towers, water towers and other high-rise buildings on the wind load and the load from its own weight. Both problems are formulated in the form of triple integral equations, which are reduced to one integral equation by the method of substitution. In the case of the axisymmetric problem, the kernel of the int

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Vatsala, Aghalaya S., and Govinda Pageni. "Series Solution Method for Solving Sequential Caputo Fractional Differential Equations." AppliedMath 3, no. 4 (2023): 730–40. http://dx.doi.org/10.3390/appliedmath3040039.

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Computing the solution of the Caputo fractional differential equation plays an important role in using the order of the fractional derivative as a parameter to enhance the model. In this work, we developed a power series solution method to solve a linear Caputo fractional differential equation of the order q,0<q<1, and this solution matches with the integer solution for q=1. In addition, we also developed a series solution method for a linear sequential Caputo fractional differential equation with constant coefficients of order 2q, which is sequential for order q with Caputo fractional i

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Ahmed, Shazad Shawki, and Shabaz Jalil MohammedFaeq. "Bessel Collocation Method for Solving Fredholm–Volterra Integro-Fractional Differential Equations of Multi-High Order in the Caputo Sense." Symmetry 13, no. 12 (2021): 2354. http://dx.doi.org/10.3390/sym13122354.

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The approximate solutions of Fredholm–Volterra integro-differential equations of multi-fractional order within the Caputo sense (F-VIFDEs) under mixed conditions are presented in this article apply a collocation points technique based completely on Bessel polynomials of the first kind. This new approach depends particularly on transforming the linear equation and conditions into the matrix relations (some time symmetry matrix), which results in resolving a linear algebraic equation with unknown generalized Bessel coefficients. Numerical examples are given to show the technique’s validity and a

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