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A new highly accurate domain decomposition optimal homotopy analysis method and its convergence for singular boundary value problems
Author(s) -
Roul Pradip,
Madduri Harshita
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5181
Subject(s) - homotopy analysis method , mathematics , convergence (economics) , homotopy , domain decomposition methods , boundary value problem , singular value decomposition , adomian decomposition method , mathematical optimization , spline (mechanical) , decomposition method (queueing theory) , domain (mathematical analysis) , decomposition , mathematical analysis , partial differential equation , algorithm , finite element method , physics , structural engineering , discrete mathematics , pure mathematics , engineering , economics , thermodynamics , economic growth , ecology , biology
We describe a new iterative technique based on domain decomposition optimal homotopy analysis method for solving singular boundary value problems arising in various physical models in applied science and technology. This method produces approximate solution in the form of a series with easily computable components. The method is analyzed for convergence. Some computational examples are presented to illustrate the applicability and efficiency of the proposed method. The advantage in the domain decomposition optimal homotopy analysis method as compared with the classical optimal homotopy analysis method is that fewer number of solution components are required to obtain similar results. Furthermore, this method shows its advantage over the spline method and the finite difference methods.