in this paper, we apply the local fractional adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of fredholm integral equations of the second kind within local fractional derivative operators. the iteration procedure is based on local fractional derivative. the obtained results reveal that the proposed methods are very efficient and simple tools ...

Computation of the internal electric field induced in human body by low-frequency power systems is time-consuming. We compute an approximate solution nearly real time using a reduced basis for field. The computed once (off-line) approximating source multipoles, coefficients which can be any position due to analytic translation and rotation formulas. results are validated with respect finite ele...

Simultaneous reactions between solids and gases are very important in the chemical and metallurgical processes. In the modeling, the chemical reaction and diffusion of gases must be considered. Therefore, a set of coupled partial differential equations is found. When the kinetic is a function of solid concentration, there is not any analytical solution for these equations. Therefore, numerical ...

We study kinetic models of reversible enzyme reactions and compare two techniques for analytic approximate solutions of the model. Analytic approximate solutions of non-linear reaction equations for reversible enzyme reactions are calculated using the Homotopy Perturbation Method (HPM) and the Simple Iteration Method (SIM). The results of the approximations are similar. The Matlab programs are ...

In this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad ‎et al., ‎‎[K. Maleknejad ‎and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, ‎Appl. Math. Comput.‎ (2005)]‎ to gain...

We give a constructive proof of the classical Cauchy–Kovalevskaya theorem for ordinary differential equations which provides sufficient condition an initial value problem to have unique, analytic solution. Our is inspired by modern numerical technique rigorously solving nonlinear problems known as radii polynomial approach. The main idea recast existence and uniqueness solutions fixed point on ...

There was an attempt to find an analytic expression3, however that paper contains an error in the application of the boundary conditions. More recently, Gelmont and Shur4, found an analytic expression for very thin substrates and presented the result of a more general numerical solution. They showed that the formula above was inaccurate for the range of the ratio of substrate thickness to conta...

We study the problem of subharmonic bifurcations for analytic systems in the plane with perturbations depending periodically on time, in the case in which we only assume that the subharmonic Melnikov function has at least one zero. If the order of zero is odd, then there is always at least one subharmonic solution, whereas if the order is even in general other conditions have to be assumed to g...