‎‎‎In this paper‎, ‎we develop multi-step methods to solve a class of two-dimensional nonlinear Volterra integral equations (2D-NVIEs) of the first kind‎. ‎Here‎, ‎we convert a 2D-NVIE of the first kind to a one-dimensional linear VIE of the first kind and then we solve the resulted equation numerically by multi-step methods‎. ‎We also verify convergence and error analysis of the method‎. ‎At t...

Here, creation of the universe is obtained out of " no matter or energy " , but only from gravity of 10-dimensional " bulk " space-time. In the beginning, the higher-derivative gravitational action is taken in (4 + D)-dimensional space-time with topology M 4 ⊗ S D , where M 4 is the usual 4-dimensional space-time and the D-dimensional sphere S D being a compact manifold. On compactification of ...

natural convection between vertical parallel plates occurs frequently in applications such as solar collectors and cooling of electronic instruments. the problem is a two dimensional developing buoyant flow. in this work, the two dimensional conservation equations are solved numerically for constant wall temperature and constant wall heat flux. the results for the local nusselt number at the du...

In this paper, we give a KAM theorem for a class of infinite dimensional nearly integrable Hamiltonian systems. The theorem can be applied to some Hamiltonian partial differential equations in higher dimensional spaces with periodic boundary conditions to construct linearly stable quasi–periodic solutions and its local Birkhoff normal form. The applications to the higher dimensional beam equati...

in the present paper, the flow and heat transfer of two types of nanofluids, namely, silver-water and silicon dioxide-water, were theoretically analyzed over an isothermal continues stretching sheet. to this purpose, the governing partial differential equations were converted to a set of nonlinear differential equations using similarity transforms and were then analytically solved. it was found...