The Magnus expansion is a frequently used tool to get approximate analytic solutions of time-dependent linear ordinary differential equations and in particular the Schrödinger equation in quantum mechanics. However, the complexity of the expansion restricts its use in practice only to the first terms. Here we introduce new and more accurate analytic approximations based on the Magnus expansion ...

In this paper two different methods are presented to approximate the solution of the fractional BlackScholes equation for valuation of barrier option. Also, the two schemes need less computational work in comparison with the traditional methods. In this work, we propose a new generalization of the two-dimensional differential transform method and decomposition method that will extend the applic...

THE THREE DIMENSIONAL FLOW PAST A STRETCHING SHEET BY EXTENDED OPTIMAL HOMOTOPY ASYMPTOTIC METHOD H. Ullah, S. Islam, M. Idrees, M. Fiza, A. Zaman Abdul Wali Khan University Mardan, 23200, Khyber Pakhtunkhwa, Pakistan ABSTRACT: In this paper Extended Optimal Homotopy Asymptotic Method (EOHAM), a new analytic approximate technique has been used to three dimensional flow past a stretching sheet. ...

We examine analytically, numerically, and experimentally the phase shift incurred by a soliton pulse when it collides with a copropagating, orthogonally polarized soliton pulse in a highly birefringent optical fiber. Use of a well-known average variational principle and a Gaussian ansatz reduces the dynamics to a set of ordinary differential equations for which an approximate analytic solution ...

Abstract – In this paper, a new approximate method has been presented to solve the linear Fredholm integral equations system (FIEs). The technique is based on, first, differentiating both sides of integral equations n times and then substituting the Taylor series the unknown functions in the resulting equation and later, transforming to a matrix equation. By merging these results, a new system ...

The nonlinear control techniques are applied to the model of rotary inverted pendulum. The model has two degrees of freedom and is not exactly linearizable. The goal is to control output trajectory of the rotary inverted pendulum asymptotically along a desired reference. Moreover, the designed controller should be robust with respect to specified perturbations and parameters uncertainties. A co...

in this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear volterra integral equations of the first-kind is proposed. this problem is transformedto a nonlinear two-dimensional volterra integral equation of the second-kind. the properties ofthe bivariate shifted legendre functions are presented. the operational matrices of integrationtogether with the produ...

In this paper, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product of a simple cosmological model in two ways: firstly, we compute it analytically via a trick; secondly, we use the complexifier coherent states to approximate the physical inner product defined by the master constraint o...

We present analytic expressions that approximate the behavior of the spacetime of a collapsing spherically symmetric scalar eld in the critical regime rst discovered by Choptuik. We nd that the critical region of spacetime can usefully be divided into a \quiescent" region and an \oscillatory" region, and a moving \transition edge" that separates the two regions. We nd that in each region the cr...