Solving nonlocal boundary value problems for first‐ and second‐order differential equations by the Adomian decomposition method

Kybernetes ◽  
2013 ◽  
Vol 42 (4) ◽  
pp. 641-664 ◽  
Author(s):  
Lazhar Bougoffa ◽  
Randolph C. Rach
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Decomposition Method ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Adomian Decomposition Method ◽  
Second Order ◽  
Nonlocal Boundary Value Problems ◽  
Second Order Differential Equations ◽  
Adomian Decomposition

scholarly journals An iterative method for solving boundary value problems for second order differential equations

2016 ◽  
Vol 12 (8) ◽  
pp. 6489-6499
Author(s):  
Ymnah Salah Alruwaily
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Second Order ◽  
Robin Boundary Conditions ◽  
Second Order Differential Equations ◽  
Adomian Decomposition ◽  
Robin Boundary

The purpose of this paper is to investigate the application of the Adomian decomposition method (ADM) for solving boundary value problems for second-order differential equations with Robin boundary conditions. We first reformulate the boundary value problems for linear equations as a fixed point problems for a linear Fredholm integral operator, and then apply the ADM. We also extend our approach to include second-order nonlinear differential equations subject Robin boundary conditions.

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