Relevant bibliographies by topics / Integro-differential equation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
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Academic literature on the topic 'Integro-differential equation'

Author: Grafiati
Published: 4 June 2021
Last updated: 13 June 2025

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Journal articles on the topic "Integro-differential equation"

1

Yuldashev, T. K., and S. K. Zarifzoda. "On a New Class of Singular Integro-differential Equations." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 101, no. 1 (2021): 138–48. http://dx.doi.org/10.31489/2021m1/138-148.

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In this paper for a new class of model and non-model partial integro-differential equations with singularity in the kernel, we obtained integral representation of family of solutions by aid of arbitrary functions. Such type of integro-differential equations are different from Cauchy-type singular integro-differential equations. Cauchy-type singular integro-differential equations are studied by the methods of the theory of analytic functions. In the process of our research the new types of singular integro-differential operators are introduced and main property of entered operators are learned. It is shown that the solution of studied equation is equivalent to the solution of system of two equations with respect to x and y, one of which is integral equation and the other is integro-differential equation. Further, non-model integro-differential equations are studied by regularization method. This regularization method for non-model equation is based on selecting and analysis of a model part of the equation and reduced to the solution of two second kind Volterra type integral equations with weak singularity in the kernel. It is shown that the presence of a non-model part in the equation does not affect to the general structure of the solutions. From here investigation of the model equations for given class of the integro-differential equations becomes important. In the cases, when the solution of given integro-differential equation depends on any arbitrary functions, a Cauchy type problems are investigated.
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Tunç, Cemil, and Osman Tunç. "On the Fundamental Analyses of Solutions to Nonlinear Integro-Differential Equations of the Second Order." Mathematics 10, no. 22 (2022): 4235. http://dx.doi.org/10.3390/math10224235.

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In this article, a scalar nonlinear integro-differential equation of second order and a non-linear system of integro-differential equations with infinite delays are considered. Qualitative properties of solutions called the global asymptotic stability, integrability and boundedness of solutions of the second-order scalar nonlinear integro-differential equation and the nonlinear system of nonlinear integro-differential equations with infinite delays are discussed. In the article, new explicit qualitative conditions are presented for solutions of both the second-order scalar nonlinear integro-differential equations with infinite delay and the nonlinear system of integro-differential equations with infinite delay. The proofs of the main results of the article are based on two new Lyapunov–Krasovski functionals. In particular cases, the results of the article are illustrated with three numerical examples, and connections to known tests are discussed. The main novelty and originality of this article are that the considered integro-differential equation and system of integro-differential equations with infinite delays are new mathematical models, the main six qualitative results given are also new.
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Wang, Shuyi, and Fanwei Meng. "Ulam Stability of n-th Order Delay Integro-Differential Equations." Mathematics 9, no. 23 (2021): 3029. http://dx.doi.org/10.3390/math9233029.

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In this paper, the Ulam stability of an n-th order delay integro-differential equation is given. Firstly, the existence and uniqueness theorem of a solution for the delay integro-differential equation is obtained using a Lipschitz condition and the Banach contraction principle. Then, the expression of the solution for delay integro-differential equation is derived by mathematical induction. On this basis, we obtain the Ulam stability of the delay integro-differential equation via Gronwall–Bellman inequality. Finally, two examples of delay integro-differential equations are given to explain our main results.
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Karkarashvili, G. S. "Fredholm integro-differential equation." Journal of Soviet Mathematics 66, no. 3 (1993): 2236–42. http://dx.doi.org/10.1007/bf01229590.

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Fedorov, V. E., A. D. Godova, and B. T. Kien. "Integro-differential equations with bounded operators in Banach spaces." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 106, no. 2 (2022): 93–107. http://dx.doi.org/10.31489/2022m2/93-107.

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The paper investigates integro-differential equations in Banach spaces with operators, which are a composition of convolution and differentiation operators. Depending on the order of action of these two operators, we talk about integro-differential operators of the Riemann—Liouville type, when the convolution operator acts first, and integro-differential operators of the Gerasimov type otherwise. Special cases of the operators under consideration are the fractional derivatives of Riemann—Liouville and Gerasimov, respectively. The classes of integro-differential operators under study also include those in which the convolution has an integral kernel without singularities. The conditions of the unique solvability of the Cauchy type problem for a linear integro-differential equation of the Riemann—Liouville type and the Cauchy problem for a linear integrodifferential equation of the Gerasimov type with a bounded operator at the unknown function are obtained. These results are used in the study of similar equations with a degenerate operator at an integro-differential operator under the condition of relative boundedness of the pair of operators from the equation. Abstract results are applied to the study of initial boundary value problems for partial differential equations with an integro-differential operator, the convolution in which is given by the Mittag-Leffler function multiplied by a power function.
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ZARIFZODA, Sarvar K., and Raim N. ODINAEV. "INVESTIGATION OF SOME CLASSES OF SECOND ORDER PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS WITH A POWERLOGARITHMIC SINGULARITY IN THE KERNEL." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 67 (2020): 40–54. http://dx.doi.org/10.17223/19988621/67/4.

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For a class of second-order partial integro-differential equations with a power singularity and logarithmic singularity in the kernel, integral representations of the solution manifold in terms of arbitrary constants are obtained in the class of functions vanishing with a certain asymptotic behavior. Although the kernel of the given equation is not a Fredholm type kernel, the solution of the studied equation in a class of vanishing functions is found in an explicit form. We represent a second-order integro-differential equation as a product of two first-order integro-differential operators. For these one-dimensional integro-differential operators, in the cases when the roots of the corresponding characteristic equations are real and different, real and equal and complex and conjugate, the inverse operators are found. It is found that the presence of power singularity and logarithmic singularity in the kernel affects the number of arbitrary constants in the general solution. This number, depending on the roots of the corresponding characteristic equations, can reach nine. Also, the cases when the given integro-differential equation has a unique solution are found. The correctness of the obtained results with the help of the detailed solutions of concrete examples are shown. The method of solving the given problem can be used for solving model and nonmodel integro-differential equations with a higher order power singularity and logarithmic singularity in the kernel.
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Yüzbaşi, Şuayip. "A shifted Legendre method for solving a population model and delay linear Volterra integro-differential equations." International Journal of Biomathematics 10, no. 07 (2017): 1750091. http://dx.doi.org/10.1142/s1793524517500917.

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In this paper, we propose a collocation method to obtain the approximate solutions of a population model and the delay linear Volterra integro-differential equations. The method is based on the shifted Legendre polynomials. By using the required matrix operations and collocation points, the delay linear Fredholm integro-differential equation is transformed into a matrix equation. The matrix equation corresponds to a system of linear algebraic equations. Also, an error estimation method for method and improvement of solutions is presented by using the residual function. Applications of population model and general delay integro-differential equation are given. The obtained results are compared with the known results.
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Nazarova, K. "ON ONE METHOD FOR OBTAINING UNIQUE SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR AN INTEGRO-DIFFERENTIAL EQUATION." Q A Iasaýı atyndaǵy Halyqaralyq qazaq-túrіk ýnıversıtetіnіń habarlary (fızıka matematıka ınformatıka serııasy), no. 1 (March 15, 2022): 42–54. http://dx.doi.org/10.47526/2022-2/2524-0080.04.

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The modified method of parametrization is used to study a linear Fredholm integro-differential equation with a degenerate kernel. Using the fundamental matrix, the conditions are established for the existence of a solution to the special Cauchy problem for the Fredholm integro-differential equation with a degenerate kernel. A system of linear algebraic equations is constructed with respect to the introduced additional parameters. Conditions for the unique solvability of a linear boundary value problem for the Fredholm integro-differential equation with a degenerate kernel are obtained.
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Melville, John. "A Linear Integro-Differential Equation." SIAM Review 33, no. 4 (1991): 655–56. http://dx.doi.org/10.1137/1033142.

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Burova, I. G., and Yu K. Demyanovich. "Nonlenear Integro-differential Equations and Splines of the Fifth Order of Approximation." WSEAS TRANSACTIONS ON MATHEMATICS 21 (September 23, 2022): 691–700. http://dx.doi.org/10.37394/23206.2022.21.81.

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In this paper, we consider the solution of nonlinear Volterra–Fredholm integro-differential equation, which contains the first derivative of the function. Our method transforms the nonlinear Volterra-Fredholm integro-differential equations into a system of nonlinear algebraic equations. The method based on the application of the local polynomial splines of the fifth order of approximation is proposed. Theorems about the errors of the approximation of a function and its first derivative by these splines are given. With the help of the proposed splines, the function and the derivative are replaced by the corresponding approximation. Note that at the beginning, in the middle and at the end of the interval of the definition of the integro-differential equation, the corresponding types of splines are used: the left, the right or the middle splines of the fifth order of approximation. When using the spline approximations, we also obtain the corresponding formulas for numerical differentiation. which we also apply for the solution of integro-differential equations. The formulas for approximation of the function and its derivative are presented. The results of the numerical solution of several integro-differential equations are presented. The proposed method is shown that it can be applied to solve integro-differential equations containing the second derivative of the solution.
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Dissertations / Theses on the topic "Integro-differential equation"

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Medlock, Jan P. "Integro-differential-equation models in ecology and epidemiology /." Thesis, Connect to this title online; UW restricted, 2004. http://hdl.handle.net/1773/6790.

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Kurniawan, Budi. "Numerical solution of Prandtl's lifting-line equation /." Title page, contents and summary only, 1992. http://web4.library.adelaide.edu.au/theses/09SM/09smk78.pdf.

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Bhowmik, Samir Kumar. "Numerical approximation of a nonlinear partial integro-differential equation." Thesis, Heriot-Watt University, 2008. http://hdl.handle.net/10399/2199.

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Lattimer, Timothy Richard Bislig. "Singular partial integro-differential equations arising in thin aerofoil theory." Thesis, University of Southampton, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.243192.

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Hao, Han. "Traveling Wave Solutions of Integro-differential Equations of One-dimensional Neuronal Networks." Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/24244.

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Traveling wave solutions of integro-differential equations for modeling one-dimensional neuronal networks, are studied. Under moderate continuity assumptions, necessary and sufficient conditions for the existence and uniqueness of monotone increasing (decreasing) traveling wave solutions are established. Some faults in previous studies are corrected.
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Al-Jawary, Majeed Ahmed Weli. "The radial integration boundary integral and integro-differential equation methods for numerical solution of problems with variable coefficients." Thesis, Brunel University, 2012. http://bura.brunel.ac.uk/handle/2438/6449.

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The boundary element method (BEM) has become a powerful method for the numerical solution of boundary-value problems (BVPs), due to its ability (at least for problems with constant coefficients) of reducing a BVP for a linear partial differential equation (PDE) defined in a domain to an integral equation defined on the boundary, leading to a simplified discretisation process with boundary elements only. On the other hand, the coefficients in the mathematical model of a physical problem typically correspond to the material parameters of the problem. In many physical problems, the governing equation is likely to involve variable coefficients. The application of the BEM to these equations is hampered by the difficulty of finding a fundamental solution. The first part of this thesis will focus on the derivation of the boundary integral equation (BIE) for the Laplace equation, and numerical results are presented for some examples using constant elements. Then, the formulations of the boundary-domain integral or integro-differential equation (BDIE or BDIDE) for heat conduction problems with variable coefficients are presented using a parametrix (Levi function), which is usually available. The second part of this thesis deals with the extension of the BDIE and BDIDE formulations to the treatment of the two-dimensional Helmholtz equation with variable coefficients. Four possible cases are investigated, first of all when both material parameters and wave number are constant, in which case the zero-order Bessel function of the second kind is used as fundamental solution. Moreover, when the material parameters are variable (with constant or variable wave number), a parametrix is adopted to reduce the Helmholtz equation to a BDIE or a BDIDE. Finally, when material parameters are constant (with variable wave number), the standard fundamental solution for the Laplace equation is used in the formulation. In the third part, the radial integration method (RIM) is introduced and discussed in detail. Modifications are introduced to the RIM, particularly the fact that the radial integral is calculated by using a pure boundary-only integral which relaxes the “star-shaped” requirement of the RIM. Then, the RIM is used to convert the domain integrals appearing in both BDIE and BDIDE for heat conduction and Helmholtz equations to equivalent boundary integrals. For domain integrals consisting of known functions the transformation is straightforward, while for domain integrals that include unknown variables the transformation is accomplished with the use of augmented radial basis functions (RBFs). The most attractive feature of the method is that the transformations are very simple and have similar forms for both 2D and 3D problems. Finally, the application of the RIM is discussed for the diffusion equation, in which the parabolic PDE is initially reformulated as a BDIE or a BDIDE and the RIM is used to convert the resulting domain integrals to equivalent boundary integrals. Three cases have been investigated, for homogenous, non-homogeneous and variable coefficient diffusion problems.
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Ahlip, Rehez Ajmal. "Stability & filtering of stochastic systems." Thesis, Queensland University of Technology, 1997.

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Nagamine, Andre. "Solução numérica de equações integro-diferenciais singulares." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-27052009-102500/.

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A Teoria das equações integrais, desde a segunda metade do século XX, tem assumido um papel cada vez maior no âmbito de problemas aplicados. Com isso, surge a necessidade do desenvolvimento de métodos numéricos cada vez mais eficazes para a resolução deste tipo de equação. Isso tem como consequência a possibilidade de resolução de uma gama cada vez maior de problemas. Nesse sentido, outros tipos de equações integrais estão sendo objeto de estudos, dentre elas as chamadas equações integro-diferenciais. O presente trabalho tem como objetivo o estudo das equações integro-diferenciais singulares lineares e não-lineares. Mais especificamente, no caso linear, apresentamos os principais resultados necessários para a obtenção de um método numérico e a formulação de suas propriedades de convergência. O caso não-linear é apresentado através de um modelo matemático para tubulações em um tipo específico de reator nuclear (LMFBR) no qual origina-se a equação integro-diferencial. A partir da equação integro-diferencial um modelo numérico é proposto com base nas condições físicas do problema<br>The theory of the integral equations, since the second half of the 20th century, has been assuming an ever more important role in the modelling of applied problems. Consequently, the development of new numerical methods for integral equations is called for and a larger range of problems has been possible to be solved by these new techniques. In this sense, many types of integral equations have been derived from applications and been the object of studies, among them the so called singular integro-differential equation. The present work has, as its main objective, the study of singular integrodifferential equations, both linear and non-linear. More specifically, in the linear case, we present our main results regarding the derivation of a numerical method and its uniform convergence properties. The non-linear case is introduced through the mathematical model of boiler tubes in a specific type of nuclear reactor (LMFBR) from which the integro-differential equation originates. For this integro-differential equation a numerical method is proposed based on the physical conditions of the problem
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Kawagoe, Daisuke. "Regularity of solutions to the stationary transport equation with the incoming boundary data." Kyoto University, 2018. http://hdl.handle.net/2433/232413.

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Dareiotis, Anastasios Constantinos. "Stochastic partial differential and integro-differential equations." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/14186.

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In this work we present some new results concerning stochastic partial differential and integro-differential equations (SPDEs and SPIDEs) that appear in non-linear filtering. We prove existence and uniqueness of solutions of SPIDEs, we give a comparison principle and we suggest an approximation scheme for the non-local integral operators. Regarding SPDEs, we use techniques motivated by the work of De Giorgi, Nash, and Moser, in order to derive global and local supremum estimates, and a weak Harnack inequality.
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Books on the topic "Integro-differential equation"

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Jumarhon, B. High order product integration methods for a nonlinear Volterra integro-differential equation. University of Salford Department of Mathematics and Computer Science, 1995.

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Yeffet, Amir. A non-dissipative staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Yeffet, Amir. A non-dissipative staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Yeffet, Amir. A non-dissipative staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Yeffet, Amir. A non-dissipative staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Yeffet, Amir. A non-dissipative staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Grigoriev, Yurii N., Nail H. Ibragimov, Vladimir F. Kovalev, and Sergey V. Meleshko. Symmetries of Integro-Differential Equations. Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-90-481-3797-8.

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Lakshmikantham, V. Theory of integro-differential equations. Gordon and Breach Science Publishers, 1995.

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Singh, Harendra, Hemen Dutta, and Marcelo M. Cavalcanti, eds. Topics in Integral and Integro-Differential Equations. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-65509-9.

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1952-, Kalitvin Anatolij S., and Zabreĭko P. P. 1939-, eds. Partial integral operators and integro-differential equations. M. Dekker, 2000.

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Book chapters on the topic "Integro-differential equation"

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Das, Tapan Kumar. "Integro-Differential Equation." In Theoretical and Mathematical Physics. Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2361-0_9.

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Grigoriev, Yurii N., Nail H. Ibragimov, Vladimir F. Kovalev, and Sergey V. Meleshko. "The Boltzmann Kinetic Equation and Various Models." In Symmetries of Integro-Differential Equations. Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-90-481-3797-8_3.

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Day, William Alan. "Trigonometric Solutions of the Integro-differential Equation." In Springer Tracts in Natural Philosophy. Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4613-9555-3_3.

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Amosov, A., and G. Panasenko. "Homogenization of the Integro-Differential Burgers Equation." In Integral Methods in Science and Engineering, Volume 1. Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4899-2_1.

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Etchegaray, C., B. Grec, B. Maury, N. Meunier, and L. Navoret. "An Integro-Differential Equation for 1D Cell Migration." In Integral Methods in Science and Engineering. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16727-5_17.

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Elhagary, M. A. "Boundary Integral Equation Formulation for Fractional Order Theory of Thermo-Viscoelasticity." In Topics in Integral and Integro-Differential Equations. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-65509-9_6.

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Pandey, Ram K., and Harendra Singh. "An Efficient Numerical Algorithm to Solve Volterra Integral Equation of Second Kind." In Topics in Integral and Integro-Differential Equations. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-65509-9_8.

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Naskar, Sanjib, Souvik Kundu, and R. Gayen. "An Integral Equation Method for Wave Scattering by a Pair of Horizontal Porous Plates." In Topics in Integral and Integro-Differential Equations. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-65509-9_9.

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Day, William Alan. "Approximation by Way of the Heat Equation or the Integro-differential Equation." In Springer Tracts in Natural Philosophy. Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4613-9555-3_4.

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Gorgisheli, Sveta, Maia Mrevlishvili, and David Natroshvili. "Localized Boundary-Domain Integro-Differential Equations Approach for Stationary Heat Transfer Equation." In Applications of Mathematics and Informatics in Natural Sciences and Engineering. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56356-1_12.

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Conference papers on the topic "Integro-differential equation"

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Belakroum, Dounia, and Kheireddine Belakroum. "Sinc approximation solution of integro-differential equation." In THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5136180.

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Al-Saif, Nahdh S. M. "Neural Network for Solving Integro Partial Differential Equation." In 2022 2nd International Conference on Computing and Machine Intelligence (ICMI). IEEE, 2022. http://dx.doi.org/10.1109/icmi55296.2022.9873771.

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Mikaeilvand, Nasser, Sakineh Khakrangin, and Tofigh Allahviranloo. "Solving fuzzy Volterra integro-differential equation by fuzzy differential transform method." In 7th conference of the European Society for Fuzzy Logic and Technology. Atlantis Press, 2011. http://dx.doi.org/10.2991/eusflat.2011.56.

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Takači, Djurdjica, Virginia S. Kiryakova, and Arpad Takači. "Operational and approximate solutions of a fractional integro-differential equation." In 39TH INTERNATIONAL CONFERENCE APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS AMEE13. AIP, 2013. http://dx.doi.org/10.1063/1.4854786.

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Lope, Jose Ernie C., and Mark Philip F. Ona. "Holomorphic and Gevrey solutions of a singular integro-differential equation." In PROCEEDINGS OF THE 7TH SEAMS UGM INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATIONS 2015: Enhancing the Role of Mathematics in Interdisciplinary Research. AIP Publishing LLC, 2016. http://dx.doi.org/10.1063/1.4940830.

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Yuldashev, Tursun K. "On a Volterra type fractional integro-differential equation with degenerate kernel." In INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0057135.

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"On a nonlinear integro-differential equation with a sum-difference kernel." In Уфимская осенняя математическая школа - 2022. 2 часть. Baskir State University, 2022. http://dx.doi.org/10.33184/mnkuomsh2t-2022-09-28.4.

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Huang, Qinghua, and Wei-Chau Xie. "Stability of SDOF Nonlinear Viscoelastic System Under the Excitation of Wide-Band Noise." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-42071.

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The stochastic stability of a single degree-of-freedom (SDOF) nonlinear viscoelastic system under the excitation of wide-band noise is studied in this paper. An example of such a system is the transverse vibration of a viscoelastic column under the excitation of stochastic axial compressive load. The equation of motion is an integro-differential equation with parametric excitation. The stochastic averaging method and averaging method for integro-differential equations are applied to reduce the system. The largest Lyapunov exponents and stochastic bifurcation are studied after the averaged sytem is obtained.
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Pingzhou Liu and Qing-Long Han. "Stability analysis of recurrent neural networks - a Volterra integro-differential equation approach." In 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601). IEEE, 2004. http://dx.doi.org/10.1109/cdc.2004.1429669.

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Khairullin, Ermek. "About one special boundary value problem for multidimensional parabolic integro-differential equation." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4959707.

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Reports on the topic "Integro-differential equation"

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Caraus, Lurie, and Zhilin Li. A Direct Method and Convergence Analysis for Some System of Singular Integro-Differential Equations. Defense Technical Information Center, 2003. http://dx.doi.org/10.21236/ada451436.

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