A method for approximate solution of initial value and spectral problems one dimensional Dirac equation based on an analytic approximation the transmutation operator is presented. In fact problem numerical solutions reduced to potential matrix by a finite linear combination valued functions related generalized formal powers introduced in [16]. Convergence rate estimates terms smoothness are pro...

this paper presents an efficient modification of the variational iteration method for solvingboundary value problems using the chebyshev polynomials. the proposed method can be applied to linearand nonlinear models. the scheme is tested for some examples and the obtained results demonstrate thereliability and efficiency of the proposed method.

In this study, bymeans of homotopyperturbationmethod (HPM) an approximate analytical solution of the magnetohydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell (UCM) fluid over a porous stretching sheet is obtained. The main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to solve. HPM produces analytical expressions for the sol...

In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series exponential instead algebraic function independent variables. As consequence: i) the convergence found to be faster than same obtained by few other methods and ii) ...

We consider the quark–anti-quark potential on the three sphere or the generalized cusp anomalous dimension in planar N = 4 SYM. We concentrate on the vacuum potential in the near BPS limit with L units of R-charge. Equivalently, we study the anomalous dimension of a super-Wilson loop with L local fields inserted at a cusp. The system is described by a recently proposed infinite set of non-linea...

According to the assumption that si = sj for i = j, the matrix (5) has an inverse and the system (2) and (4) can be solved. We denote by V the Vandermonde determinant of the matrix (5) and by Vk the Vandermonde determinant of order (n − 1) of the variables s1, . . . , sk−1, sk+1, . . . , sn. We also denote by Φ r the fundamental symmetric function of the r-th order of (n − 1) variables s1, . . ...

where λ, μ1, μ2, . . . , μk, y0 ∈ C, has been studied by numerous authors e.g., 1–8 . Secondorder versions of this equation have also been studied e.g., 9, 10 . The enduring interest in this equation is due partially to the number of applications it has found such as a current collection system for an electric locomotive, cell growth models, biology, economy, control, and electrodynamics e.g., ...

The integrability of N = (2, 2) dilaton supergravity in two dimensions is studied by the use of the graded Poisson Sigma model approach. Though important differences compared to the purely bosonic models are found, the general analytic solutions are obtained. The latter include minimally gauged models as well as an ungauged version. BPS solutions are an especially interesting subclass. bergamin...

one of the ecient and powerful schemes to solve linear and nonlinear equationsis homotopy analysis method (ham). in this work, we obtain the approximate solution ofa system of partial dierential equations (pdes) by means of ham. for this purpose, wedevelop the concept of ham for a system of pdes as a matrix form. then, we prove theconvergence theorem and apply the proposed method to nd the a...