본문 바로가기
KERD
논문KCI 등재

Solutions of a class of singular second-order IVPs by variational homotopy perturbation method

2

조회

0

다운로드

0

인용

0

참고문헌

주제분류수학

초록

In this Letter, solutions of a class of singular initial value problems (IVPs)in the second-order ordinary differential equations (ODEs) by Variational homotopy perturbation method (VHPM) are presented. The singularity behavior that occurs at the point x = 0 is the main difficulty in the analysis of these equations. In fact, we employ the VHPM to this model of equations to overcome the singularity behavior at the point x = 0.

Abstract

In this Letter, solutions of a class of singular initial value problems (IVPs)in the second-order ordinary differential equations (ODEs) by Variational homotopy perturbation method (VHPM) are presented. The singularity behavior that occurs at the point x = 0 is the main difficulty in the analysis of these equations. In fact, we employ the VHPM to this model of equations to overcome the singularity behavior at the point x = 0.

참고문헌 (27)

  1. He, J.H., "Variational iteration method-a kind of non-linear analitycal technique: some examples", International Journal of Non-Linear Mechanics, 34(4), pp.699~708 (1999)
  2. He, J.H., "Variational iteration method: new development and applications", Computers and Mathematics with Applications, 54(7), pp.881~894 (2007)
  3. Inokuti, M., "General use of the Lagrange multiplier in nonlinear mathematical physics. in: Variational method in the mechanics of solids", pp.156~162 (1978), Pergamon press
  4. He, J.H., "Non-perturbative method for strongly nonlinear problems", pp.2006
  5. Abdou, M.A., "Variation iteration method for solving Burger's and coupled Burger's equation", Journal of Computational and Applied Mathematics, 181(2), pp.245~251 (2005)
  6. Bildik, N., "The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations", International Journal of Nonlinear Sciences and Numerical Simulation, 7(1), pp.65~70 (2006)
  7. He, J.H., "Some asymptotic methods for strongly nonlinear equations", International Journal of Modern Physics B, 20(10), pp.1141~1199 (2006)
  8. He, J.H., "Homotopy perturbation technique", Computer Methods in Applied Mechanics and Engineering, 178(3), pp.257~262 (1999)
  9. He, J.H., "Homotopy perturbation method for solving boundary value problems", Physics Letters A, 350(1), pp.87~88 (2006)
  10. He, J.H., "Comparison of homotopy perturbation method and homotopy analysis method", Applied Mathematics and Computation, 156(2), pp.527~539 (2004)
  11. He, J.H., "Homotopy perturbation method for bifurcation of nonlinear problems", International Journal of Nonlinear Sciences and numerical Simulation, 6(2), pp.207~208 (2005)
  12. He, J.H., "The homotopy perturbation method nonlinear oscillators with discontinuities", Applied Mathematics and Computation, 151(1), pp.287~292 (2004)
  13. He, J.H., "A coupling method of a homotopy tachnique and a perturbation technique for nonlinear problems", International Journal of Non-Linear Mechanics, 35(1), pp.37~43 (2000)
  14. Batiha, Kh., "Approximate Analytical Solutions For Time-dependent Emden-Fowler-Type Equations By Variational Iteration Method", Am. J. Applied Sci, 4(7), pp.439~443 (2007)
  15. Noor, M.A., "Variational Homotopy Perturbation Method for solving Higher Dimentional initial boundary value problems", Mathematical Problems in Engineering (2008)
  16. Noor, M.A., "Variational iteration method for unsteady flow of gas through a porous medium using He's polynomials and Pade approximants", Computers and Mathematics with Applications (2009)
  17. Noor, M.A., "Modified variational iteration technique for solving singular fourth-order parabolic partial differential equations", Nonlinear Analysis (2008)
  18. Chandrasekhar, S., "Introduction to the Study of Stellar Structure" (1967), Dover
  19. Davis, H.T., "Introduction to Nonlinear Differential and Integral Equations" (1962), Dover
  20. Richardson, O.U., "The Emission of Electricity from Hot Bodies" (1921), Zongmans Green and Company
  21. Chowdhury, M.S.H., "Solutions of a class of singular secondorder IVPs by homotopy-perturbation method", Physics Letters A, 365, pp.439~447 (2007)
  22. Shawagfeh, N.T., "Nonperturbative approximate solution for Lane-Emden equation", J. Math. Phys, 34(9), pp.4364~4369 (1993)
  23. Wazwaz, A.M., "A new algorithm for solving differential equations of Lane-Emden type", Appl. Math. Comput, 118, pp.287~310 (2001)
  24. Wazwaz, A.M., "A new method for solving singular initial value problems in the second-order ordinary differential equations", Appl. Math. Comput, 128, pp.45~57 (2002)
  25. Wazwaz, A.M., "The modified decomposition method for analytic treatment of differential equationse", Appl. Math. Comput, 173, pp.165~176 (2006)
  26. Adomian, G., "Solution of physical problems by decomposition", Comput. Math. Appl, 27(9), pp.145~154 (1994)
  27. Chowdhury, M.S.H., "Solutions of EmdenFowler equations by homotopy perturbation method", Nonlinear Analysis: Real World Applications, 10, pp.104~115 (2009)

관련 논문AI추천

이 간행물의 다른 논문 (13건)