An Explicit Cubic Iteration

Compact alternating group explicit method for the cubic spline solution of two point boundary value problems with significant nonlinear first derivative terms

In this paper, we report the application of two parameter coupled alternating group explicit (CAGE) iteration and Newton-CAGE iteration methods for the cubic spline solution of non-linear differential equation u" = f(r,u,u') subject to given natural boundary conditions. The error analysis for CAGE iteration method is discussed in details. We compared the results of proposed CAGE iteration metho...

The Hermite Cubic Collocation Approximation to the EigenValues and the Eigenfuntions of the Laplace Operator

Piecewise Hermite cubics have been widely used in a variety of ways for solving partial differential equations. For a number of these techniques, knowledge about the Hermite cubic collocation approximations to the spectrum of the Laplace operator is often very useful, for error analysis and, a fortiori, possible iteration parameters. To this end, we givc here explicit closed-form expressions fo...

Analysis of Higher Spin Field Equations in Four Dimensions

The minimal bosonic higher spin gauge theory in four dimensions contains massless particles of spin s = 0, 2, 4, .. that arise in the symmetric product of two spin 0 singletons. It is based on an infinite dimensional extension of the AdS4 algebra a la Vasiliev. We derive an expansion scheme in which the gravitational gauge fields are treated exactly and the gravitational curvatures and the high...

A composite explicit iterative process with a viscosity method for Lipschitzian semigroup in a smooth Banach space

Misiurewicz points for polynomial maps and transversality

The behavior under iteration of the critical points of a polynomial map plays an essential role in understanding its dynamics. We study the special case where the forward orbits of the critical points are finite. Thurston’s theorem tells us that fixing a particular critical point portrait and degree leads to only finitely many possible polynomials (up to equivalence) and that, in many cases, th...

Revisiting Implicit Finite Difference Schemes for Three-Dimensional Room Acoustics Simulations on GPU

Implicit finite difference schemes for the 3-D wave equation using a 27-point stencil on the cubic grid are presented, for use in room acoustics modelling and artificial reverberation. The system of equations that arises from the implicit formulation is solved using the Jacobi iterative method. Numerical dispersion is analysed and computational efficiency is compared to second-order accurate 27...