Picard and Adomian methods for quadratic integral equation

By A. El-Sayed, H. Hashem, E. Ziada. 2010

54 citations recorded by the source corpus.

We are concerning with two analytical methods; the classical method of successive approximations (Picard method) [14] which consists the construction of a sequence of functions such that the limit of this sequence of functions in the sense of uniform convergence is the solution of a quadratic integral equation, and Adomian method which gives the solution as a series see ([1-6], [12] and [13]). The existence and uniqueness of the solution and the convergence will be discussed for each method. Mathematical subject classification: Primary: 39B82; Secondary: 44B20, 46C05.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/3db9d359e7d8a76150e1fc500e672336f762820b

Citations in the corpus

• Numerical solution of nonlinear partial quadratic integro‐differential equations of fractional order via hybrid of block‐pulse and parabolic functions (2018, unknown): “More recently, several articles have been published on the numerical solution of quadratic integral equations, including Adomian decomposition method and repeated trapezoidal methods [11], Picard and Adomian methods [12], modified hat functions method [13], and variational iteration method and homot”