In this study, a new root-finding method for solving nonlinear equations is proposed. This method requires two starting values that do not necessarily bracketing a root. However, when the starting values are selected to be close to a root, the proposed method converges to the root quicker than the secant method. Another advantage over all iterative methods is that; the proposed method usually c...

An iterative formula based on Newton’s method alone is presented for the iterative solutions of equations that ensures convergence in cases where the traditional NewtonMethodmay fail to converge to the desired root. In addition, themethod has super-quadratic convergence of order 2.414 (i.e., 1 + √2). Newton method is said to fail in certain cases leading to oscillation, divergence to increasing...

Solving optimal control problems for nonlinear partial differential equations represents a significant numerical challenge due to the tremendous size and possible model difficulties (e.g., nonlinearities) of the discretized problems. In this paper, a novel space-mapping technique for solving the aforementioned problem class is introduced, analyzed, and tested. The advantage of the space-mapping...

This paper presents two new controllers and uses an extension of the generalized secant method of solving linear equations. 1] The rst controller is adaptive and operates in the time domain. The second one is a learning-adaptive controller which uses a similar mathematical concept, but it is formulated to deal with repetitive systems with repetitive disturbances. This controller operates in the...

In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...

Conjugate gradient methods are widely used for unconstrained optimization, especially large scale problems. Most of conjugate gradient methods don’t always generate a descent search direction, so the descent condition is usually assumed in the analyses and implementations. Dai and Yuan (1999) proposed the conjugate gradient method which generates a descent direction at every iteration. Yabe and...

From position and velocity coordinates for several given instants, it is possible to determine orbital elements for the preliminary orbit. This theoretical trajectory, also known as keplerian orbit, is defined taking only into account mutual gravitational attraction forces between both bodies, the Earth and the satellite. Nevertheless it should be refined with later observations from ground sta...