Solution of non linear Fredholm integral equation involving constant delay by BEM with piecewise linear approximation

References

• M. Mosleh and M. Otadi , Least squares approximation method for the solution of Hammerstein-Volterra delay integral equation, Applied Mathematics and Computation ,258, pp. 105-110, (2015). doi: 10.1016/j.amc.2015.01.100
   Web of Science ®Google Scholar
• A. Alturk , The regularization-homotopy method for the two-dimensional Fredholm integral equations of the first kind, Mathematical and Computational Application , 21, 9, pp. 1-10, (2016).
   Google Scholar
• A.M. Denisov , Approximation of quasi-solutions of Fredholm’s equation of first kind with a kernel of special form, USSR Comput. Math. and Math. Phys ., 11, 5, pp. 269-276, (1971). doi: 10.1016/0041-5553(71)90051-6
   Google Scholar
• A.M. Denisov , On the order of approximation when solving a Fredholm equation of the first kind with a kernel of special type, USSR Comput Math. and Math. Phys ., 13,1, pp. 255-260, (1973). doi: 10.1016/0041-5553(74)90019-6
   Google Scholar
• C. T. Artikis , A. P. Voudouri , T. P. Artikis , Incorporating an Integral equation for characteristic functions in investigating a class of distributions, Journal of Statistics and Management Systems , 19,1, pp. 89-97, (2016). doi: 10.1080/09720510.2015.1033866
   Web of Science ®Google Scholar
• Y. Mahmoudi , Taylor polynomial solution of non-linear Volterra Fredholm integral equation, International Journal of Computer Mathematics , 82, 7, pp. 881-887, (2005). doi: 10.1080/00207160512331331110
   Web of Science ®Google Scholar
• M. Sezer and S. Dogan , Chebyshev series solutions of Fredholm integral equations, International Journal of Mathematical Education in Science and Technology , 27, 5, pp. 649-657, (1996). doi: 10.1080/0020739960270503
   Google Scholar
• B.N. Mandal and S. Bhattacharyya , Numerical solution of some classes of integral equations using Bernstein polynomials, Applied Mathematics and Computation , pp 1707-1716, (2007). doi: 10.1016/j.amc.2007.02.058
   Google Scholar
• B.N. Mandal and S. Bhattacharyya , Numerical solution of a singular integro-differential equation, Applied Mathematics and Computation , 195, pp. 346-350, (2008). doi: 10.1016/j.amc.2007.04.103
   Web of Science ®Google Scholar
• A. Alturk , Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem, Springer Plus , 5, pp. 1-15, (2016). doi: 10.1186/s40064-016-3645-8
   PubMedGoogle Scholar
• C. Pozrikidis , A Practical Guide to Boundary Element Methods with the Software Library, BEMLIB, London : CRC Press, (2002).
   Google Scholar
• Min-Chie Chiu , Shape optimization of double-chamber side mufflers with extended tube by using four-pole matrix, boundary element method and genetic algorithm, Journal of Information and Optimization Sciences , 29,1, pp.81-101, (2008) doi: 10.1080/02522667.2008.10699792
   Google Scholar
• S. Banerjee , R. Chakraborty and A. Samanta , Boundary element approach of solving Fredholm and Voltera integral equations, Int. J. Mathematical Modeling and Numerical Optimisation , 9,1, pp. 1-9, (2019). doi: 10.1504/IJMMNO.2019.096907
   Google Scholar
• K. Holmberg , Solving the staircase cost facility location problem with decomposition and piecewise linearization, European Journal of Operational Research , 75, 1, pp. 41-61, (1994). doi: 10.1016/0377-2217(94)90184-8
   Web of Science ®Google Scholar
• Abdul Majid Wazwaz , Linear and Non linear Integral Equations methods and Applications, Springer, (2011).
   Google Scholar