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Though many numerical methods have been put for nonlinear equations, their convergence and performance are highly sensitive to the initial guesses of the solution pre-supplied. However, the selection of good initial guess is often of hard work. Aiming at this, a novel approach is proposed to resolve nonlinear equations. It takes genetic algorithms' new achievement differential evolution algorithms...
In this paper, we use homotopy method to transfer nonlinear equations to a differential equations, then we apply four-order Runge-Kutta method to solve the differential equations for getting a more stable and easily convergent solution. What is more important, we demonstrate a complete proof of the whole process, which provide a scientific foundation for the method as a whole. In the end, we give...
The paper describes an algorithm that determines the solutions of a n-dimensional nonlinear equation system within a given interval. The result is based on Semenov algorithm that isolates the solutions and improves upon it by introducing Kantorovich existence criterion. In Semenov algorithm the existence of the solution is decided by applying Newton method on each interval containing at most one solution...
In this paper, a new family of combined iterative methods for the solution of nonlinear equations is presented.The new family of methods is based on Newton's method and the family of sixth-order iterative methods developed by Chun. Per iteration the new methods require three evaluations of the function and two evaluations of its first derivative. Numerical tests show that it takes less number of iterations...
We present some modified Newton-type methods for solving nonlinear equations. These algorithms are free from second derivatives and permit f'(x) = 0 in some iteration points. The convergent analysis demonstrates that the order of convergence and the efficiency index of the present methods are better than that of the classical Newton's method. Some numerical examples are given to illustrate their efficiency...
In this paper, fixed-final time-constrained optimal control laws using neural networks (NNS) to solve Hamilton-Jacobi-Bellman (HJB) equations for general affine in the constrained nonlinear systems are proposed. An NN is used to approximate the time-varying cost function using the method of least squares on a predefined region. The result is an NN nearly -constrained feedback controller that has time-varying...
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