an:05949971
Zbl 1221.65343
Shidfar, A.; Molabahrami, A.; Babaei, A.; Yazdanian, A.
A series solution of the nonlinear Volterra and Fredholm integro-differential equations
EN
Commun. Nonlinear Sci. Numer. Simul. 15, No. 2, 205-215 (2010).
00286511
2010
j
65R20 45J05
homotopy analysis method; series solution; integro-differential equation; Volterra; Fredholm
Summary: The homotopy analysis method is applied to obtained the series solution of the high-order nonlinear Volterra and Fredholm integro-differential problems with power-law nonlinearity. Two cases are considered, in the first case the set of base functions is introduced to represent solution of given nonlinear problem and in the other case, the set of base functions is not introduced. However, in both cases, the convergence-parameter provides us with a simple way to adjust and control the convergence region of solution series.