We investigate effectiveness of an acceleration method applied to the modified Picard iteration for simulations of variably saturated flow. We solve nonlinear systems using both unaccelerated and accelerated modified Picard iteration as well as Newton’s method. Since Picard iterations can be slow to converge, the advantage of acceleration is to provide faster convergence while maintaining advan...

This paper demonstrates a study on some significant latest innovations in the approximated techniques to find the approximate solutions of Caputo fractional Volterra-Fredholm integro-differential equations. To this aim, the study uses the modified Adomian decomposition method (MADM) and the modified variational iteration method (MVIM). A wider applicability of these techniques are based on thei...

For further insight into the perturbation technique within framework of asymptotic iteration method (PAIM), we suggest this to be used as an alternative traditional well-known techniques. We show by means very simple algebraic manipulations that PAIM can directly applied obtain symbolic expectation value any perturbed potential piece without using eigenfunction unperturbed problem. One fundamen...

In this paper, heat and mass transfer in the unsteady squeezing flow between parallel plates is analyzed using a perturbation-iteration algorithm. The similarity transformation is used to transform the governing partial differential equations into ordinary differential equations, before being solved. The solutions of the velocity, temperature and concentration are derived and sketched to explai...