This paper presents an application of the nonlinear optimal control techniques to the design of launch vehicle autopilots. The optimal control is given by the solution to the Hamilton-Jacobi-Bellman (HJB) equation, which in this case cannot be solved explicity. A method based upon Successive Galerkin Approximation (SGA), is used to obtain an approximate optimal solution. Simulation results invo...

In this article we have considered a non-standard finite difference method for the solution of second order  Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the Fredholm integro-differential equation into a system of equations. We have also developed a numerical met...

Multi-criteria shortest path problems (MSPP) are called as NP-Hard. For MSPPs, a unique solution for optimizing all the criteria simultaneously will rarely exist in reality. Algorithmic and approximation schemes are available to solve these problems; however, the complexity of these approaches often prohibits their implementation on real-world applications. This paper describes the development ...

This paper focuses on a hydraulic radius separation approach used to calculate the boundary shear stress in terms of bed and wall shear stress proposed in a trapezoidal channel. The average bed and sidewall shear stress in smooth trapezoidal open channels are derived after using Guo & Julien (2005) early equations taking a part of an investigation to cover both rectangular and trapezoidal chann...

Often when we talk about an approximation algorithm, we give an approximation ratio. The approximation ratio gives the ratio between our solution and the actual solution. The goal is to obtain an approximation ratio as close to 1 as possible. If the problem involves a minimization, the approximation ratio will be greater than 1; if it involves a maximization, the approximation ratio will be les...

In recent years, Fuzzy differential equations are very useful indifferent sciences such as physics, chemistry, biology and economy. It should be noted, that if the equations that appear to be uncertain, then take help of fuzzy logic at these equations. Considering that most of the time analytic solution of such equations and finding an exact solution has either high complexity or cannot be solv...