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.

Boundary value problems for systems of second order differential equations

1985 ◽  
Vol 101 (1-2) ◽  
pp. 61-76 ◽  
Author(s):  
L. H. Erbe ◽  
H. W. Knobloch
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Existence Of A Solution ◽  
Differential Systems ◽  
Second Order Differential Equations

SynopsisWe consider boundary value problems for second order differential systems of the form (1)x” = A(t)x′ + f(t, x) and (2) x” = A(t)x′ + f(t, x) + q(t, x). By assuming the existence of a solution to (1) with a given region in (t, x) space, we derive conditions under which there exists a solution to (2) which stays in a certain neighbourhood of and satisfies given boundary conditions.

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