‎The ‎method ‎of ‎quasilinearization ‎is ‎an ‎effective ‎tool ‎to ‎solve nonlinear ‎equations ‎when ‎some ‎conditions‎ on ‎the ‎nonlinear term ‎of ‎the ‎problem ‎are ‎satisfi‎‎ed. ‎W‎hen ‎the ‎conditions ‎hold, ‎applying ‎this ‎techniqu‎e ‎gives ‎two ‎sequences of ‎coupled ‎linear ‎equations‎ and ‎the ‎solutions ‎of ‎th‎ese ‎linear ‎equations ‎are quadratically ‎convergent ‎to ‎the ‎solution ‎o...

in this paper, a nonlinear volterra-fredholm integral equation of the first kind is solved by using the homotopy analysis method (ham). in this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by ham. the approximate solution of this equation is calculated in the form of a series which its components are computed easily. the accuracy...

in this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the maclaurin series of the exact solution. nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. these equations equip a significant mathematical model for dynamical systems. the accuracy o...

Abstract We provide a rigorous mathematical framework to establish the hydrodynamic limit of Vlasov model introduced in Takata and Noguchi (J. Stat. Phys. 172:880-903, 2018) by order describe phase transition fluids kinetic equations. prove that, when scale parameter tends 0, this converges nonlocal Cahn-Hilliard equation with degenerate mobility. For our analysis, we introduce apropriate forms...

this study was carried out to obtain quantitative relationships between zn in equilibrium solution and that retained by 20 calcareous soils. soils were brought into equilibrium with varying solution concentrations of zn, and the amounts removed from solution were used to check the fit to six adsorption isotherms, namely, freundlich, langmuir, temkin, gunary, two surface langmuir and adjusted fr...