An SQP method for optimal control of weakly singular Hammerstein integral equations

1996 ◽  
Vol 33 (3) ◽  
pp. 227-252 ◽  
Author(s):  
W. Alt ◽  
R. Sontag ◽  
F. Tr�ltzsch
Keyword(s):  
Optimal Control ◽  
Integral Equations ◽  
Sqp Method ◽  
Hammerstein Integral Equations ◽  
Weakly Singular

scholarly journals A New Direct Method for Solving Nonlinear Volterra-Fredholm-Hammerstein Integral Equations via Optimal Control Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
M. A. El-Ameen ◽  
M. El-Kady
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Integral Equations ◽  
Simple Form ◽  
Existence And Uniqueness ◽  
Direct Method ◽  
New Method ◽  
Fredholm Integral Equations ◽  
Hammerstein Integral Equations

A new method for solving nonlinear Volterra-Fredholm-Hammerstein (VFH) integral equations is presented. This method is based on reformulation of VFH to the simple form of Fredholm integral equations and hence converts it to optimal control problem. The existence and uniqueness of proposed method are achieved. Numerical results are given at the end of this paper.

scholarly journals Numerical solvability of a class of Volterra-Hammerstein integral equations with noncompact kernels

2005 ◽  
Vol 2005 (2) ◽  
pp. 171-181 ◽  
Author(s):  
M. Hadizadeh ◽  
M. Mohamadsohi
Keyword(s):  
Integral Equations ◽  
Singular Integral Equations ◽  
Nonlinear Functions ◽  
Product Integration ◽  
Existence And Uniqueness Results ◽  
Hammerstein Integral Equations ◽  
Uniqueness Results ◽  
Weakly Singular ◽  
Weakly Singular Integral Equations ◽  
Theoretical Results

We study the numerical solvability of a class of nonlinear weakly singular integral equations of Volterra-Hammerstein type with noncompact kernels. We obtain existence and uniqueness results and analyze the product integration methods for these equations under some verifiable conditions on the kernels and nonlinear functions. The convergence analysis is investigated and finally numerical experiments are given, which confirm our theoretical results.

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