TY - JOUR
T1 - Reliable algorithms for solving integro-differential equations with applications
AU - Alawneh, Ameen
AU - Al-Khaled, Kamel
AU - Al-Towaiq, Mohammed
PY - 2010/6
Y1 - 2010/6
N2 - This paper suggests four different methods to solve nonlinear integro-differential equations, namely, He's variational iteration method, Adomian decomposition method, He's homotopy perturbation method and differential transform method. To assess the accuracy of each method, a test example with known exact solution is used. The study outlines significant features of these methods as well as sheds some light on advantages of one method over the other. The results show that these methods are very efficient, convenient and can be adapted to fit a larger class of problems. The comparison reveals that, although the numerical results of these methods are similar, He's homotopy perturbation method is the easiest, the most efficient and convenient. Moreover, we applied modified forms of He's variational iteration method and differential transform method to solve a mathematical model, which describes the accumulated effect of toxins on populations living in a closed system.
AB - This paper suggests four different methods to solve nonlinear integro-differential equations, namely, He's variational iteration method, Adomian decomposition method, He's homotopy perturbation method and differential transform method. To assess the accuracy of each method, a test example with known exact solution is used. The study outlines significant features of these methods as well as sheds some light on advantages of one method over the other. The results show that these methods are very efficient, convenient and can be adapted to fit a larger class of problems. The comparison reveals that, although the numerical results of these methods are similar, He's homotopy perturbation method is the easiest, the most efficient and convenient. Moreover, we applied modified forms of He's variational iteration method and differential transform method to solve a mathematical model, which describes the accumulated effect of toxins on populations living in a closed system.
KW - Adomian decomposition method
KW - Differential transform method
KW - Homotopy perturbation method
KW - Nonlinear integro-differential equations
KW - Population growth
KW - Variational iteration method
UR - http://www.scopus.com/inward/record.url?scp=77953274985&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77953274985&partnerID=8YFLogxK
U2 - 10.1080/00207160802385818
DO - 10.1080/00207160802385818
M3 - Article
AN - SCOPUS:77953274985
SN - 0020-7160
VL - 87
SP - 1538
EP - 1554
JO - International Journal of Computer Mathematics
JF - International Journal of Computer Mathematics
IS - 7
ER -