A numerical solution of the modified Burgers' equation (MBE) is obtained by using quartic B-spline subdomain finite element method (SFEM) over which the nonlinear term is locally linearized and using quartic B-spline differential quadrature (QBDQM) method. The accuracy and efficiency of the methods are discussed by computing L 2 and L ∞ error norms. Comparisons are made with those of some earli...

In this paper we provide the guidelines for the direct degree elevation of NURBS curves. Through the analysis of linear equation systems of quartic and lower degree splines we derive a direct relation between the knot vector of a spline and the degree elevation coefficients. We also present a direct degree elevation scheme and several algorithms based on the discovered relation. Experimental re...

One might say that this formula allows one to solve the quadratic with a pencil. There is an analogous formula for the general quartic equation, ax+ bx + cx + dx+ e = 0. If you just have to know the formula or one way to derive it and don’t care about anything else, you may just skip to the last section of this paper. However, there is a mathematical notion of a pencil, which is rather cool and...

We give a class of exact solutions of quartic scalar field theories. These solutions prove to be interesting as are characterized by the production of mass contributions arising from the nonlinear terms while maintaining a wavelike behavior. So, a quartic massless equation has a nonlinear wave solution with a dispersion relation of a massive wave and a quartic scalar theory gets its mass term r...

We consider the evolution of optical solitons inside a nonlinear dispersive fiber with random birefringence, causing polarization-mode dispersion. We convert the pair of coupled nonlinear Schrödinger equations satisfied by the orthogonally polarized components into a Fokker-Planck equation using the collective-variable approach. We solve this equation and derive expressions for the probability ...

Quartic-Spline Collocation Methods for Fourth-Order Two-Point Boundary Value Problems Ying Zhu Master of Science Graduate Department of Computer Science University of Toronto 2001 This thesis presents numerical methods for the solution of general linear fourth-order boundary value problems in one dimension. The methods are based on quartic splines, that is, piecewise quartic polynomials with C3...

The purpose of this paper is to solve the seventh-order functional equation as follows:  --------------------------- Next, we study the stability of this type of functional equation. Clearly, the function ----------  holds in this type functional equation. Also, we prove Hyers-Ulam stability for this type functional equation in the β-Gaussian Banach space.