A semi-empirical mathematical model for predicting the physical part of ignition delay period in the combustion of diesel engines with swirl is developed. This model is based on a single droplet evaporation model. The governing equations, namely, equations of droplet motion, heat and mass transfer were solved simultaneously using a Runge-Kutta step by step method. The computation was executed u...

<p style='text-indent:20px;'>In this paper, we study the nonlocal problem for pseudo-parabolic equation with time and space fractional derivatives. The derivative is of Caputo type order <inline-formula><tex-math id="M1">\begin{document}$ \sigma,\; \; 0<\sigma<1 $\end{document}</tex-math></inline-formula> id="M2">\begin{document}$ \alpha,\beta &amp...

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...