A coupled method of Laplace transform and Legendre wavelets is presented to obtain exact solutions of Lane-Emden-type equations. By employing properties of Laplace transform, a new operator is first introduced and then its Legendre wavelets operational matrix is derived to convert the Lane-Emden equations into a system of algebraic equations. Block pulse functions are used to calculate the Lege...

In this paper, a computational technique is proposed for solving a nonlinear backward stochastic differential equation involving standard Brownian motion. The method is presented via the block pulse functions in combination with the collocation method. With using this approach, the nonlinear backward stochastic differential is reduced to a stochastic nonlinear system of 2m equations and 2m unkn...

In this report the transient rocking response of electrical equipment subjected to trigonometric pulses and near-source ground motions is investigated in detail. First the rocking response of a rigid block subjected to a half-sine pulse motion is reviewed. It is shown that the solution presented by Housner (1963) for the minimum acceleration amplitude of a half-sine pulse that is needed to over...

Based on using block-pulse functions (BPFs)/shifted Legendre polynomials (SLPs) a unified approach for computing optimal control law of linear time-invariant/time-varying time-delay free/time-delay dynamic systems with quadratic performance index is discussed in this paper. The governing delay-differential equations of dynamic systems are converted into linear algebraic equations by using the o...

We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid "noise terms" is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed fo...

Since various problems in science and engineering fields can be modeled by nonlinear Volterra-Fredholm integral equations, the main focus of this study is to present an effective numerical method for solving them. This method is based on the hybrid functions of Legendre polynomials and block-pulse functions. By using this approach, a nonlinear Volterra-Fredholm integral equation reduces to a no...