Quasilinearization of the Initial Value Problem for Difference Equations with “Maxima”

The object of investigation of the paper is a special type of difference equations containing the maximum value of the unknown function over a past time interval. These equations are adequate models of real processes which present state depends significantly on their maximal value over a past time interval. An algorithm based on the quasilinearization method is suggested to solve approximately the initial value problem for the given difference equation. Every successive approximation of the unknown solution is the unique solution of an appropriately constructed initial value problem for a linear difference equation with “maxima,” and a formula for its explicit form is given. Also, each approximation is a lower/upper solution of the given mixed problem. It is proved the quadratic convergence of the successive approximations. The suggested algorithm is realized as a computer program, and it is applied to an example, illustrating the advantages of the suggested scheme

Some recent results in aerospace vehicle trajectory optimization techniques

Algorithms and computation techniques for solving trajectory optimization problem

Guidance, flight mechanics and trajectory optimization. Volume 13 - Numerical optimization methods

Three numerical procedures for Mayer classical and non-classical problems in trajectory optimizatio

Variable time optimal control

Computational algorithms and techniques for solving variable time optimal control problem

Use of variable lift control to optimize aerodynamic braking for a Mars entry vehicle

Variable lift control to obtain maximum velocity reduction through aerodynamic braking for Mars entr

Optimal control of distributed parameter systems using multilevel techniques

Optimal control of distributed parameter systems using multilevel technique

Monotone-Iterative Method for Solving Antiperiodic Nonlinear Boundary Value Problems for Generalized Delay Difference Equations with Maxima

A nonlinear generalized difference equation with both delays and the maximum value of the unknown function over a discrete past time interval are studied. A nonlinear boundary value problem of antiperiodic type for the given difference equation is set up. One of the main characteristics of the considered difference equation is the presence of the unknown function in both sides of the equation. It leads to impossibility for using the step method for explicit solving of the nonlinear difference equation. In this paper, an approximate method, namely, the monotone iterative technique, is applied to solve the problem. An important feature of the given algorithm is that each successive approximation of the unknown solution is equal to the unique solution of an appropriately constructed initial value problem for a linear difference equation with “maxima,” and an algorithm for its explicit solving is given. Also, each approximation is a lower/upper solution of the given nonlinear boundary value problem. The suggested scheme for approximate solving is computer realized, and it is applied to a particular example, which is a generalization of a model in population dynamics

Quasilinearization program for determining optimum finite-thrust transfers between inclined orbits

Quasi-linearization program for boundary value problem of minimum fuel orbital transfe