Advertisement

The Emerging Solution for Partial Differential Problems

  • P. V. Ramana
  • Vivek Singh
Conference paper

Abstract

In this paper, we present a technique for solving ordinary and partial differential equations (ODE and PDE) linear and nonlinear by an emerging method. The emerging method consists of decomposing a given differential equation into linear, nonlinear and remainder terms. The method has been applied quite extensively by mathematicians for various cases. However, engineering applications are not that many. While applying the method to a static plate and static problem we observed that the solution with emerging one very close to numerical and analytical solutions. An emerging method has been applied for linear equation plate problems to improve the simplicity, accuracy and convergence of above mentioned problems. The plate problems can easily be solved with help of emerging method, which is decomposition technique and semi-analytical method. The decomposition emerging method results are found to converge very quickly and are more close to exact solution.

Keywords

Emerging decomposition method Partial differential Plate Matlab 

References

  1. 1.
    Adomian G (1984) Convergent series solutions of nonlinear equations. Comput Appl Math 11(2):225–230CrossRefMathSciNetzbMATHGoogle Scholar
  2. 2.
    Adomian G (1994) Solving frontier problems of physics: the decomposition method, 2nd edn. Kluwer, DordrechtCrossRefzbMATHGoogle Scholar
  3. 3.
    Morawetz CS (1991) The decay of solution of the exterior initial boundary value problem for the wave equations. Pure Appl Math 14:561–568CrossRefMathSciNetGoogle Scholar

Bibliography

  1. 4.
    Lewy H, Stampacchia G (1969) On the regularity of the solutions of the variational inequalities. Commun Pure Appl Math 22:153–188CrossRefMathSciNetzbMATHGoogle Scholar
  2. 5.
    Al-Said EA, Noor MA (1998) Numerical solutions of a system of fourth order boundary value problems. Int J Comput Math 71:347–355MathSciNetGoogle Scholar
  3. 6.
    Khalifa AK, Noor MA (1990) Quintic splines solutions of a class of contact problems. Math Comput Model 13:51–58CrossRefMathSciNetzbMATHGoogle Scholar
  4. 7.
    Noor MA, Al-Said EA (2000) Numerical solutions of fourth order variational inequalities. Int J Comput Math 75:107–116CrossRefMathSciNetzbMATHGoogle Scholar
  5. 8.
    Noor, Li J-L (2009) Adomian’s decomposition method and homotopy perturbation method in solving nonlinear equations. J Comput Appl Math 228(1):168–173CrossRefMathSciNetGoogle Scholar
  6. 9.
    Al-Said EA, Noor MA (2002) Quartic spline method for solving fourth order obstacle boundary value problem. Appl Math Comput 43:107–116CrossRefMathSciNetGoogle Scholar
  7. 10.
    Noor MA, Tirmizi SI (1986) Numerical methods for unilateral problems. J Comput Appl Math 16:387–395CrossRefMathSciNetzbMATHGoogle Scholar
  8. 11.
    Noor MA, Tirmizi SI (1991) Numerical methods for a class of contact problems. Int J Eng Sci 29:513–521CrossRefMathSciNetzbMATHGoogle Scholar
  9. 12.
    Repaci A (1990) Nonlinear dynamical systems: on the accuracy of Adomian’s decomposition method. Appl Math Lit 3:35–39CrossRefMathSciNetzbMATHGoogle Scholar
  10. 13.
    Wazwaz AM (2002) A new method for solving singular initial value problems in the second order ordinary differential equations. Appl Math Comput 128:45–57CrossRefMathSciNetzbMATHGoogle Scholar
  11. 14.
    Aluru N (2000) A point collocation method based on reproducing kernel approximations. Int J Numer Meth Eng 47:1083–1121CrossRefzbMATHGoogle Scholar
  12. 15.
    Reddy JN (1995) An introduction to the finite element method. McGraw Hill Book Company, New YorkGoogle Scholar

Copyright information

© Springer India 2015

Authors and Affiliations

  • P. V. Ramana
    • 1
  • Vivek Singh
    • 2
  1. 1.Department of Civil EngineeringNational Center for Disaster Management and Mitigation (NCDMM)BlairsvilleUSA
  2. 2.Malaviya National Institute of Technology (MNIT)JaipurIndia

Personalised recommendations