Approximate Solution of Nonlinear Fredholm Integral Equations of the First Kind via Converting to Optimization Problems
In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To
this purpose, we consider two stages of approximation.
First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems
and optimal control problems. Finally numerical examples is
proposed.
[1] A. H. Borzabadi, A. V. Kamyad, and H. H. Mehne, "A different approach for solving the nonlinear Fredholm integral equations of the second kind", Applied Mathematics and Computation, No.
173, 724735,2006.
[2] L. M. Delves, "A fast method for the solution of fredholm
integral equations", J. Inst. Math. Appl., Vol. 20, 173-182, 1977.
[3] L. M. Delves and J. L. Mohamed, "Computational Methods for
Integral Equations", Cambridge Univ. Press, 1985.
[4] L. M. Delves and J. Walsh, "Numerical Solution of Integral
Equations", Oxford Univ. Press, 1974.
[5] S. Effati and A. V. Kamyad, "Solution of boundary value problems
for linear second orderODE-s by using measure theory", J.
Analysis, Vol. 6, pp.139-149, 1998.
[6] M. Gachpazan, A. Kerachian and A. V. Kamyad, "A new Method
for solving nonlinear second order differential equations", Korean
J. Comput. Appl. Math., Vol. 7, No. 2, pp. 333-345, 2000.
[7] A. J. Jerri, "Introduction to Integral Equations with Applications",
London: Wiley, 1999.
[8] W. Rudin, "Principles of Mathematical Analysis", 3rd ed,
McGraw-Hill, New York, 1976.
[1] A. H. Borzabadi, A. V. Kamyad, and H. H. Mehne, "A different approach for solving the nonlinear Fredholm integral equations of the second kind", Applied Mathematics and Computation, No.
173, 724735,2006.
[2] L. M. Delves, "A fast method for the solution of fredholm
integral equations", J. Inst. Math. Appl., Vol. 20, 173-182, 1977.
[3] L. M. Delves and J. L. Mohamed, "Computational Methods for
Integral Equations", Cambridge Univ. Press, 1985.
[4] L. M. Delves and J. Walsh, "Numerical Solution of Integral
Equations", Oxford Univ. Press, 1974.
[5] S. Effati and A. V. Kamyad, "Solution of boundary value problems
for linear second orderODE-s by using measure theory", J.
Analysis, Vol. 6, pp.139-149, 1998.
[6] M. Gachpazan, A. Kerachian and A. V. Kamyad, "A new Method
for solving nonlinear second order differential equations", Korean
J. Comput. Appl. Math., Vol. 7, No. 2, pp. 333-345, 2000.
[7] A. J. Jerri, "Introduction to Integral Equations with Applications",
London: Wiley, 1999.
[8] W. Rudin, "Principles of Mathematical Analysis", 3rd ed,
McGraw-Hill, New York, 1976.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:52212", author = "Akbar H. Borzabadi and Omid S. Fard", title = "Approximate Solution of Nonlinear Fredholm Integral Equations of the First Kind via Converting to Optimization Problems", abstract = "In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To
this purpose, we consider two stages of approximation.
First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems
and optimal control problems. Finally numerical examples is
proposed.", keywords = "Fredholm integral equation, Optimization method, Optimal control, Nonlinear and linear programming", volume = "1", number = "9", pages = "411-4", }