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“…These problems appeared in the theory of airfoils in fluid mechanics [1,3,11,20]. The programs have been provided by Mathematica 8.…”

confidence: 99%

“…Also, Wazwaz in [21] and Delves in [2] used this method for solving Fredholm and Volterra integral equations of the first kind. In [1], Bougoffa et al applied the regularization method with parameter to solve a given Cauchy integral equations of the first kind.…”

confidence: 99%

“…The Adomian decomposition method (ADM) is one of iterative and applicable methods for solving various problems such as the Klein-Gordon equation [29], Triki-Biswas equation [30], the problem of boundary layer convective heat transfer [31], integral equations (IEs) of the first and second kinds with hypersingular kernels [32,33], the Volterra integral form of the Lane-Emden equations with initial values and boundary conditions [34], Cauchy IEs of the first kind [35], linear and nonlinear IEs [36] and partial differential equations [37].…”

confidence: 99%

“…Indeed, Abel's integral equation is one of the most famous equations that frequently appear in many engineering problems and physical properties such as heat conduction, semiconductors, chemical reactions, and metallurgy (see, e.g., [6,7]). Besides, over the past few years, many numerical methods for solving Abel's integral equation have been developed, such as collocation methods [8], product integration methods [9,10], fractional multistep methods [11][12][13], methods based on wavelets [14][15][16], backward Euler methods [9], Adomian decomposition method [17], and Tau approximation method [18].…”

confidence: 99%

“…Mennouni and Guedjiba (2011) have also used the successive approximation method to solve the airfoil equation. The Adomain decomposition method was also used after regularization to solve airfoil equation by Bougoffa et al (2013). Setia (2014) has proposed a Bernstein polynomial-based method to solve the classical airfoil equation.…”

mentioning

confidence: 99%