Mehdi Salimi

A new class of three-point methods with optimal convergence order eight and its dynamics

We establish a new class of three-point methods for the computation of simple zeros of a scalar function. Based on the two-point optimal method by Ostrowski (1966), we construct a family of order eight methods which use three evaluations of f and one of f′ and therefore have an efficiency index equal to 84≈1.682

Evasion from many pursuers in simple motion differential game with integral constraints

\sqrt [4]{8}\approx 1.682

Pursuit-Evasion Differential Game with Many Inertial Players

and are optimal in the sense of the Kung and Traub conjecture (Kung and Traub J. Assoc. Comput. Math. 21, 634–651, 1974). Moreover, the dynamics of the proposed methods are shown with some comparisons to other existing methods. Numerical comparison with existing optimal schemes suggests that the new class provides a valuable alternative for solving nonlinear equations.

New modification of Maheshwari’s method with optimal eighth order convergence for solving nonlinear equations

We study a two dimensional evasion differential game with several pursuers and one evader with integral constraints on control functions of players. Assuming that the total resource of the pursuers does not exceed that of the evader, we solve the game by presenting explicit strategy for the evader which guarantees evasion.

A new class of optimal four-point methods with convergence order 16 for solving nonlinear equations

We consider pursuit-evasion differential game of countable number inertial players in Hilbert space with integral constraints on the control functions of players. Duration of the game is fixed. The payoff functional is the greatest lower bound of distances between the pursuers and evader when the game is terminated. The pursuers try to minimize the functional, and the evader tries to maximize it. In this paper, we find the value of the game and construct optimal strategies of the players.

On a Fixed Duration Pursuit Differential Game with Geometric and Integral Constraints

Abstract In this paper, we present a family of three-point with eight-order convergence methods for finding the simple roots of nonlinear equations by suitable approximations and weight function based on Maheshwari’s method. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. These class of methods have the efficiency index equal to 814≈1.682

Optimal Newton–Secant like methods without memory for solving nonlinear equations with its dynamics

{8^{{\textstyle{1 \over 4}}}} \approx 1.682

A Dynamic Stackelberg Game of Supply Chain for a Corporate Social Responsibility

. We describe the analysis of the proposed methods along with numerical experiments including comparison with the existing methods. Moreover, the attraction basins of the proposed methods are shown with some comparisons to the other existing methods.

Pursuit-evasion game of many players with coordinate-wise integral constraints on a convex set in the plane

We introduce a new class of optimal iterative methods without memory for approximating a simple root of a given nonlinear equation. The proposed class uses four function evaluations and one first derivative evaluation per iteration and it is therefore optimal in the sense of Kung and Traubs conjecture. We present the construction, convergence analysis and numerical implementations, as well as comparisons of accuracy and basins of attraction between our method and existing optimal methods for several test problems.

Approximate solutions by artificial neural network of hybrid fuzzy differential equations

In this paper we investigate a differential game in which countably many dynamical objects pursue a single one. All the players perform simple motions. The duration of the game is fixed. The controls of a group of pursuers are subject to integral constraints, and the controls of the other pursuers and the evader are subject to geometric constraints. The payoff of the game is the distance between the evader and the closest pursuer when the game is terminated. We construct optimal strategies for players and find the value of the game.