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Approximate and Analytic Solution of Some Nonlinear Diffusive Equations

  • Amitha Manmohan Rao
  • Arundhati Suresh Warke
Chapter
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 41)

Abstract

Nonlinear partial differential equations (PDEs) have wide range of applications in mathematics, science and engineering and are used in modelling various types of problems arising in fluid mechanics. This paper presents the numerical approximation of some nonlinear diffusive PDEs; Newell–Whitehead–Segel (NWS) equation and Burgers’ equation by using Laplace decomposition method (LDM) and finite difference method(FDM). The nonlinear PDEs are considered to study the influence of the parameters like initial condition and dissipative coefficient on the solution, wave distortion, and wave propagation. The numerical results obtained are analysed graphically. The approach can be extended to obtain physically relevant solutions to a wide range of nonlinear PDEs describing various real life phenomena involving nonlinear and dissipative effects. MATLAB-R2017b is used for all the computations and graphical representation.

Keywords

Adomian polynomials Approximate solution FDM Nonlinear PDE NWS equation LDM 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Amitha Manmohan Rao
    • 1
    • 2
  • Arundhati Suresh Warke
    • 3
  1. 1.Symbiosis International (Deemed University)PuneIndia
  2. 2.N.S.S. College of Commerce & EconomicsAffiliated to University of MumbaiMumbaiIndia
  3. 3.Symbiosis Institute of TechnologyPuneIndia

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