Monotonicity methods for two classes of nonlinear boundary value problems with semilinear first order elliptic systems in the plane

1982 ◽  
Vol 109 (1) ◽  
pp. 215-238 ◽  
Author(s):  
L. V. Wolfersdorf
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Elliptic Systems ◽  
Nonlinear Boundary Value Problems ◽  
First Order ◽  
Nonlinear Boundary Value ◽  
Monotonicity Methods

scholarly journals A new analytical approach for solving nonlinear boundary value problems arising in nonlinear phenomena

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2489-2497 ◽  
Author(s):  
Liaqat Ali ◽  
Saeed Islam ◽  
Taza Gul ◽  
Ali Alshomrani ◽  
Murad Ullah
Keyword(s):  
Boundary Value Problems ◽  
Analytical Approach ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Phenomena ◽  
Nonlinear Boundary Value Problems ◽  
Unknown Parameters ◽  
Order Problem ◽  
First Order ◽  
Nonlinear Boundary Value

In this research a new analytical approach is used to solve nonlinear boundary value problems (BVPs) of higher order occurring in nonlinear phenomena. It converts a complex nonlinear problem into zeroth order and first order problem. It consists of initial guess, auxiliary functions (containing unknown convergence controlling parameters) and a homotopy. The unknown parameters are determined by minimizing the residual. Many methods which are explained in this paper are used to determine these parameters. Here Galerkin?s method is used for this purpose. It is applied to solve non-linear BVPs of fourth and fifth order. The results are compared with the already existing methods e.g., Galerkin?s Method with Quintic B-splines, Differential Transform Method (DTM), and Optimal Homotopy AsymptoticMethod (OHAM). It gives efficient and accurate first-order approximate solution. The results achieved by this technique are in excellent concurrence with the exact solution and hence proved that this method is effective and easy to apply.

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