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Relevant bibliographies by topics / Integral Equation Approach

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Journal articles

Academic literature on the topic 'Integral Equation Approach'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Integral Equation Approach"

1

Haslinger, Jaroslav, C. C. Baniotopoulos, and Panagiotis D. Panagiotopoulos. "A boundary multivalued integral “equation” approach to the semipermeability problem." Applications of Mathematics 38, no. 1 (1993): 39–60. http://dx.doi.org/10.21136/am.1993.104533.

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Şenel, Ayşe Anapalı, Yalçın Öztürk, and Mustafa Gülsu. "New Numerical Approach for Solving Abel’s Integral Equations." Foundations of Computing and Decision Sciences 46, no. 3 (2021): 255–71. http://dx.doi.org/10.2478/fcds-2021-0017.

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Abstract In this article, we present an efficient method for solving Abel’s integral equations. This important equation is consisting of an integral equation that is modeling many problems in literature. Our proposed method is based on first taking the truncated Taylor expansions of the solution function and fractional derivatives, then substituting their matrix forms into the equation. The main character behind this technique’s approach is that it reduces such problems to solving a system of algebraic equations, thus greatly simplifying the problem. Numerical examples are used to illustrate t

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3

WHITFIELD, A. H., and N. MESSALI. "Integral-equation approach to system identification." International Journal of Control 45, no. 4 (1987): 1431–45. http://dx.doi.org/10.1080/00207178708933819.

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4

KNOBLES, D. P., S. A. STOTTS, R. A. KOCH, and T. UDAGAWA. "INTEGRAL EQUATION COUPLED MODE APPROACH APPLIED TO INTERNAL WAVE PROBLEMS." Journal of Computational Acoustics 09, no. 01 (2001): 149–67. http://dx.doi.org/10.1142/s0218396x01000449.

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A two-way coupled mode approach based on an integral equation formalism is applied to sound propagation through internal wave fields defined at the 1999 Shallow Water Acoustics Modeling Workshop. Solutions of the coupled equations are obtained using a powerful approach originally introduced in nuclear theory and also used to solve simple nonseparable problems in underwater acoustics. The basic integral equations are slightly modified to permit a Lanczos expansion to form a solution. The solution of the original set of integral equations is then easily recovered from the solution of the modifie

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5

Wei, Tao, and Mingtian Xu. "An integral equation approach to the unsteady convection–diffusion equations." Applied Mathematics and Computation 274 (February 2016): 55–64. http://dx.doi.org/10.1016/j.amc.2015.10.084.

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6

Zozulya, V. V. "Divergent Integrals in Elastostatics: General Considerations." ISRN Applied Mathematics 2011 (August 2, 2011): 1–25. http://dx.doi.org/10.5402/2011/726402.

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This article considers weakly singular, singular, and hypersingular integrals, which arise when the boundary integral equation methods are used to solve problems in elastostatics. The main equations related to formulation of the boundary integral equation and the boundary element methods in 2D and 3D elastostatics are discussed in details. For their regularization, an approach based on the theory of distribution and the application of the Green theorem has been used. The expressions, which allow an easy calculation of the weakly singular, singular, and hypersingular integrals, have been constr

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7

Abdillah, Muhammad Taufik, Berlian Setiawaty, and Sugi Guritman. "The Solution of Generalization of the First and Second Kind of Abel’s Integral Equation." JTAM (Jurnal Teori dan Aplikasi Matematika) 7, no. 3 (2023): 631. http://dx.doi.org/10.31764/jtam.v7i3.14193.

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Integral equations are equations in which the unknown function is found to be inside the integral sign. N. H. Abel used the integral equation to analyze the relationship between kinetic energy and potential energy in a falling object, expressed by two integral equations. This integral equation is called Abel's integral equation. Furthermore, these equations are developed to produce generalizations and further generalizations for each equation. This study aims to explain generalizations of the first and second kind of Abel’s integral equations, and to find solution for each equation. The method

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8

Chen, Jeng-Tzong, Chia-Chun Hsiao, and Shyue-Yuh Leu. "Null-Field Integral Equation Approach for Plate Problems With Circular Boundaries." Journal of Applied Mechanics 73, no. 4 (2005): 679–93. http://dx.doi.org/10.1115/1.2165239.

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In this paper, a semi-analytical approach for circular plate problems with multiple circular holes is presented. Null-field integral equation is employed to solve the plate problems while the kernel functions in the null-field integral equation are expanded to degenerate kernels based on the separation of field and source points in the fundamental solution. The unknown boundary densities of the circular plates are expressed in terms of Fourier series. It is noted that all the improper integrals are transformed to series sum and are easily calculated when the degenerate kernels and Fourier seri

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9

Saadeh, Rania. "Applications of Double ARA Integral Transform." Computation 10, no. 12 (2022): 216. http://dx.doi.org/10.3390/computation10120216.

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This paper describes our construction of a new double transform, which we call the double ARA transform (DARAT). Our novel double-integral transform can be used to solve partial differential equations and other problems. We discuss some fundamental characteristics of our approach, including existence, linearity, and several findings relating to partial derivatives and the double convolution theorem. DARAT can be used to precisely solve a variety of partial differential equations, including the heat equation, wave equation, telegraph equation, Klein–Gordon equation, and others, all of which are

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10

Avdonin, S. A., B. P. Belinskiy, and John V. Matthews. "Inverse problem on the semi-axis: local approach." Tamkang Journal of Mathematics 42, no. 3 (2011): 275–93. http://dx.doi.org/10.5556/j.tkjm.42.2011.916.

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We consider the problem of reconstruction of the potential for the wave equation on the semi-axis. We use the local versions of the Gelfand-Levitan and Krein equations, and the linear version of Simon's approach. For all methods, we reduce the problem of reconstruction to a second kind Fredholm integral equation, the kernel and the right-hand-side of which arise from an auxiliary second kind Volterra integral equation. A second-order accurate numerical method for the equations is described and implemented. Then several numerical examples verify that the algorithms can be used to reconstruct an

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