• 제목/요약/키워드: Volterra-Fredholm integral equations

검색결과 11건 처리시간 0.019초

THE RELIABLE MODIFIED OF LAPLACE ADOMIAN DECOMPOSITION METHOD TO SOLVE NONLINEAR INTERVAL VOLTERRA-FREDHOLM INTEGRAL EQUATIONS

  • Hamoud, Ahmed A.;Ghadle, Kirtiwant P.
    • Korean Journal of Mathematics
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    • 제25권3호
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    • pp.323-334
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    • 2017
  • In this paper, we propose a combined form for solving nonlinear interval Volterra-Fredholm integral equations of the second kind based on the modifying Laplace Adomian decomposition method. We find the exact solutions of nonlinear interval Volterra-Fredholm integral equations with less computation as compared with standard decomposition method. Finally, an illustrative example has been solved to show the efficiency of the proposed method.

A MATRIX FORMULATION OF THE MIXED TYPE LINEAR VOLTERRA-FREDHOLM INTEGRAL EQUATIONS

  • Fazeli, S.;Shahmorad, S.
    • Journal of applied mathematics & informatics
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    • 제29권5_6호
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    • pp.1409-1420
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    • 2011
  • In this paper we present an operational method for solving linear Volterra-Fredholm integral equations (VFIE). The method is con- structed based on three matrices with simple structures which lead to a simple and high accurate algorithm. We also present an error estimation and demonstrate accuracy of the method by numerical examples.

ON CERTAIN NEW NONLINEAR RETARDED INTEGRAL INEQUALITIES FOR FUNCTIONS IN TWO VARIABLES AND THEIR APPLICATIONS

  • Ma, Qing-Hua;Pecaric, Josip
    • 대한수학회지
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    • 제45권1호
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    • pp.121-136
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    • 2008
  • Some new explicit bounds on the solutions to a class of new nonlinear retarded Volterra-Fredholm type integral inequalities in two independent variables are established, which can be used as effective tools in the study of certain integral equations. Some examples of application are also indicated.

USING CROOKED LINES FOR THE HIGHER ACCURACY IN SYSTEM OF INTEGRAL EQUATIONS

  • Hashemiparast, S.M.;Sabzevari, M.;Fallahgoul, H.
    • Journal of applied mathematics & informatics
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    • 제29권1_2호
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    • pp.145-159
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    • 2011
  • The numerical solution to the linear and nonlinear and linear system of Fredholm and Volterra integral equations of the second kind are investigated. We have used crooked lines which includ the nodes specified by modified rationalized Haar functions. This method differs from using nominal Haar or Walsh wavelets. The accuracy of the solution is improved and the simplicity of the method of using nominal Haar functions is preserved. In this paper, the crooked lines with unknown coefficients under the specified conditions change the system of integral equations to a system of equations. By solving this system the unknowns are obtained and the crooked lines are determined. Finally, error analysis of the procedure are considered and this procedure is applied to the numerical examples, which illustrate the accuracy and simplicity of this method in comparison with the methods proposed by these authors.

APPROXIMATION OF SOLUTIONS THROUGH THE FIBONACCI WAVELETS AND MEASURE OF NONCOMPACTNESS TO NONLINEAR VOLTERRA-FREDHOLM FRACTIONAL INTEGRAL EQUATIONS

  • Supriya Kumar Paul;Lakshmi Narayan Mishra
    • Korean Journal of Mathematics
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    • 제32권1호
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    • pp.137-162
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    • 2024
  • This paper consists of two significant aims. The first aim of this paper is to establish the criteria for the existence of solutions to nonlinear Volterra-Fredholm (V-F) fractional integral equations on [0, L], where 0 < L < ∞. The fractional integral is described here in the sense of the Katugampola fractional integral of order λ > 0 and with the parameter β > 0. The concepts of the fixed point theorem and the measure of noncompactness are used as the main tools to prove the existence of solutions. The second aim of this paper is to introduce a computational method to obtain approximate numerical solutions to the considered problem. This method is based on the Fibonacci wavelets with collocation technique. Besides, the results of the error analysis and discussions of the accuracy of the solutions are also presented. To the best knowledge of the authors, this is the first computational method for this generalized problem to obtain approximate solutions. Finally, two examples are discussed with the computational tables and convergence graphs to interpret the efficiency and applicability of the presented method.

DECOMPOSITION METHOD FOR SOLVING NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS

  • KAMEL AL-KHALED;ALLAN FATHI
    • Journal of applied mathematics & informatics
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    • 제19권1_2호
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    • pp.415-425
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    • 2005
  • This paper outlines a reliable strategy for solving nonlinear Volterra-Fredholm integro-differential equations. The modified form of Adomian decomposition method is found to be fast and accurate. Numerical examples are presented to illustrate the accuracy of the method.

ON SOLUTIONS OF VOLTERRA-FREDHOLM INTEGRAL EQUATIONS

  • Thabet, A.A.;Alim, A.Hadi
    • Kyungpook Mathematical Journal
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    • 제29권2호
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    • pp.141-147
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    • 1989
  • The existence and uniqueness of solutions of nonlinear Volterra-Fred-holm integral equations of the more general type are investigated. The main tool employed in our analysis is the method of successive approximation based on the general idea of T.Wazewski.

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ANALYSIS OF HILFER FRACTIONAL VOLTERRA-FREDHOLM SYSTEM

  • Saif Aldeen M. Jameel;Saja Abdul Rahman;Ahmed A. Hamoud
    • Nonlinear Functional Analysis and Applications
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    • 제29권1호
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    • pp.259-273
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    • 2024
  • In this manuscript, we study the sufficient conditions for existence and uniqueness results of solutions of impulsive Hilfer fractional Volterra-Fredholm integro-differential equations with integral boundary conditions. Fractional calculus and Banach contraction theorem used to prove the uniqueness of results. Moreover, we also establish Hyers-Ulam stability for this problem. An example is also presented at the end.