The stationary points of the potential energy function of the φ⁴ model on a two-dimensional square lattice with nearest-neighbor interactions are studied by means of two numerical methods: a numerical homotopy continuation method and a globally convergent Newton-Raphson method. We analyze the properties of the stationary points, in particular with respect to a number of quantities that have bee...

This paper presents an accurate and efficient method to solve both point projection and point inversion for NURBS curves and surfaces. We first subdivide the NURBS curve or surface into a set of Bézier subcurves or patches. Based on the relationship between the test point and the control polygon of Bézier curve or the control point net of the Bézier patch, we extract candidate Bézier subcurves ...

A new approach for distributed power load flow calculation using nonlinear equations is presented. This new approach, which is similar to the Newton Raphson’s simple method, uses an inverse Jacobian matrix of initial states for the iteration process. Moreover, nonlinear quadratic equations have been used as they are more appropriate for the distributed power load flow calculation. This paper de...

This paper describes simple implementation of homotopy (also called continuation) algorithm for determining the proper resistance of the resistor to dissipate energy at a specified rate of an electric circuit. Homotopy algorithm can be considered as a developing of the classical methods in numerical computing such as Newton-Raphson and fixed point methods. In homoptopy methods, an embedding par...

Piecewise algebraic B-spline surfaces (ABS surfaces) are capable of modeling globally smooth shapes of arbitrary topology. These can be potentially applied in geometric modeling, scientific visualization, computer animation and mathematical illustration. However, real-time ray casting the surface is still an obstacle for interactive applications, due to the large amount of numerical root findin...

The aim of this article is to present a brief review and numerical comparison iterative methods applied solve the polynomial equations with real coefficients. In paper, four are compared, namely: Horner’s method, Synthetic division Chebyshev method (Proposed Method), Modified Newton Raphson Birge-Vieta which will helpful readers understand importance usefulness these methods.

The mathematical problem of reconstructing the unknown variable conductivity of an isotropic medium from a knowledge of boundary currents and voltages is an active area of mathematical research. In terms of impedance imaging the analytical problem is essentially the question 'is there only one conductivity distribution which could have produced this set of measurements?' In mathematical parlanc...