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The reliable modified of Laplace adomian decomposition method to solve nonlinear interval Volterra-Fredholm integral equations

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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.

Abstract

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.

참고문헌 (10)

  1. S.C. Akan, "On Solvability of Some Nonlinear Fractional Interval Integral Equations", Fractional Di erential Calculus, 72, pp.235~246 (2017)
  2. A. M. Jerri, "Introduction to Integral Equations with Applications" (1999), Wiley
  3. A. Hamoud, "On the Numerical Solution of Nonlinear Volterra-Fredholm Integral Equations by Variational Iteration Method", International Jour-nal of Advanced Scienti c and Technical Research, 3, pp.45~51 (2016)
  4. AHMED A. HAMOUD, "THE COMBINED MODIFIED LAPLACE WITH ADOMIAN DECOMPOSITION METHOD FOR SOLVING THE NONLINEAR VOLTERRA-FREDHOLM INTEGRO DIFFERENTIAL EQUATIONS", Journal of the Korean Society for Industrial and Applied Mathematics, 21(1), pp.17~28 (2017), 한국산업응용수학회
  5. M. Hussain, "Modi ed Laplace Decomposition Method", Applied Mathematical Sciences, 4(36), pp.1769~1783 (2010)
  6. M. Hussain, "Application of Laplace Decomposition Method on Semi-Infinite Domain, Numer Algor", Springer Science+Business Media, 56, pp.211~218 (2011)
  7. T. Vinh An, "A Note on Solutions of Interval-Valued Volterra Integral Equations", Journal of Integral Equations And Applica-tions, 26(1), pp.1~14 (2014)
  8. S. Salahshour, "Exact Solutions of Nonlinear Interval Volterra In-tegral Equations", Int. J. Industrial Mathematics, 4(4), pp.375~388 (2012)
  9. A.M. Wazwaz, "The Combined Laplace Transform-Adomian Decomposition Method for Handling Nonlinear Volterra Integro Di erential Equations", Applied Mathematics and Computation, 216, pp.1304~1309 (2010)
  10. A. M. Wazwaz, "Linear and Nonlinear Integral Equations Methods and Applica-tions" (2011), Springer

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