Solutions of system of Volterra integro‐differential equations using optimal homotopy asymptotic method

Abstract

In this paper, a powerful semianalytical method known as optimal homotopy asymptotic method (OHAM) has been formulated for the solution of system of Volterra integro‐differential equations. The effectiveness and performance of the proposed technique are verified by different numerical problems in the literature, and the obtained results are compared with Sinc‐collocation method. These results show the reliability and effectiveness of the proposed method. The proposed method does not require discretization like other numerical methods. Moreover, the convergence region can easily be controlled. The use of OHAM is simple and straightforward.

Heat and Mass Transfer of Rotational Flow of Unsteady Third-Grade Fluid over a Rotating Cone with Buoyancy Effects

“…In order to get the analytical solutions of equations ( 8) to (12), we have applied the optimal homotopy analysis method (OHAM) [19][20][21][22][23][24][25][26][27].…”

“…e main task of the existing paper is to observe the variation of heat and mass transfer on third-grade fluid flow induced by the rotating cone. e highly nonlinear ordinary differential equations of the third-grade fluid with the prescribed wall temperature conditions are solved by the optimal homotopy analysis method (OHAM) [19][20][21][22][23][24][25][26][27]. Usually, the nonlinear system of ODE is difficult to tackle with the analytical method.…”

Approximate solutions of nonlinear two‐dimensional Volterra integral equations

“…C. Cattani et al considered the Harmonic Wavelets and their fractional extension 10 . P. Agrawal et al find the solutions of system of Volterra integro‐differential equations using OHAM 11 . Liu et al gave analytical solutions of some integral fractional differential–difference equations 12 .…”

Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations

“…Nonlinear partial differential equations (PDEs) play a significant role in several scientific and engineering fields [1][2][3][4][5]. Since the discovery of the soliton in 1965 by Zabusky and Kruskal [6], many nonlinear PDEs have been derived and extensively applied in different branches of physics and applied mathematics [7][8][9][10][11][12][13][14][15][16][17]. Nonlinear PDEs appear in condensed matter, solid state physics, fluid mechanics, chemical kinetics, plasma physics, nonlinear optics, propagation of fluxion in Josephson junctions, ocean dynamics and many others [18][19][20][21][22][23][24][25][26][27].…”