In this work, we have applied Elzaki transform and He's homotopy perturbation method to solvepartial dierential equation (PDEs) with time-fractional derivative. With help He's homotopy per-turbation, we can handle the nonlinear terms. Further, we have applied this suggested He's homotopyperturbation method in order to reformulate initial value problem. Some illustrative examples aregiven in ord...

In this paper, we study the computational aspect of eigenvalue perturbation theory. In previous research, high order perturbation terms were often derived from Taylor series expansion. Computations based on such an approach can be both unstable and highly complicated. We present here with an approach based on the diierential formulation of perturbation theory where the high order perturbation c...

In this paper, we tried to accelerate the rate of convergence in solving second-order Fredholm type Integro-differential equations using a new method which is based on Improved homotopy perturbation method (IHPM) and applying accelerating parameters. This method is very simple and the result is obtained very fast.  

At low Q 2 , charm production in deep–inelastic scattering is adequately described by assuming generation in electroweak boson–light parton scattering (dominantly boson–gluon fusion) which naturally incorporates the correct threshold behaviour. At high Q 2 this description is inadequate, since it does not sum logs in Q 2 /m 2 c , and is replaced by the treatment of the charm quark as a light pa...

Wilson loops which are small deviations from straight, infinite lines, called wavy lines, are considered in the context of the AdS/CFT correspondence. A single wavy line and the connected correlation function of a straight and wavy line are considered. It is argued that, to leading order in “waviness”, the functional form of the loop is universal and the coefficient, which is a function of the ...

Only a few intertemporal optimal consumption and portfolio problems in partial and general equilibrium can be solved explicitly. It is illustrated in the paper that perturbation theory is a powerful tool for deriving approximate analytical solutions for the desired optimal policies in problems where general state dynamics are admitted and a preference for robustness is present. Starting from th...

Based on the recent developments of explicit computations at 2 loops in superstring theory in the covariant RNS formalism, we propose an explicit formula for the arbitrary loop 4-particle amplitude in superstring theory. We prove that this formula passes two very difficult tests: modular invariance and factorization. If proved, this shows that superstring theory is not only finite order by orde...

No. It is simply not plausible that cosmic acceleration could arise within the context of general relativity from a back-reaction effect of inhomogeneities in our universe, without the presence of a cosmological constant or “dark energy.” We point out that our universe appears to be described very accurately on all scales by a Newtonianly perturbed FLRW metric. (This assertion is entirely consi...

Two uid-ow problems are solved using perturbation expansions, with special emphasis on the reduction of intermediate expression swell. This is done by developing tools in Maple that contribute to the eecient representation and manipulation of large expressions. The tools share a common basis, which is the creation of a hierarchy of representation levels such that expressions located at higher l...

In this work, we analyze a one-dimensional steady-state Poisson-Nernst-Planck type model for ionic flow through a membrane channel with fixed boundary ion concentrations (charges) and electric potentials. We consider two ion species, one positively charged and one negatively charged, and assume zero permanent charge. A local hard-sphere potential that depends pointwise on ion concentrations is ...