where the second order differential operator F is of Hamilton-Jacobi-Bellman (HJB) type, that is, F is a supremum of linear elliptic operators, f is sublinear in u at infinity, and Ω ⊂ R is a regular bounded domain. HJB operators have been the object of intensive study during the last thirty years – for a general review of their theory and applications we refer to [26], [33], [43], [14]. Well-k...

A new generalized nonlinear variational-like inequality is introduced and studied. By applying the auxiliary principle technique and KKM theory, we construct a new iterative algorithm for solving the generalized nonlinear variational-like inequality. By means of the Banach fixed-point theorem, we establish the existence and uniqueness of solution for the generalized nonlinear variational-like i...

This paper is concerned with the existence of travelling wave solutions in a class of delayed reaction–diffusion systems without monotonicity, which concludes two-species diffusion–competition models with delays. Previous methods do not apply in solving these problems because the reaction terms do not satisfy either the so-called quasimonotonicity condition or non-quasimonotonicity condition. B...

Aerosol modelling is very important to study and simulate the behavior of aerosol dynamics in atmospheric environment. In this paper, we consider the general nonlinear aerosol dynamic equations which describe the evolution of the aerosol distribution. Continuous time and discrete time wavelet Galerkin methods are proposed for solving this problem. By using the Schauder’s fixed point theorem and...

this paper presents some results concerning the existence of solutions for a functional integral equation of volterra type in two variables, via measure of noncompactness. two examples are included to illustrate the main result.

We use the visualization and animation capabilities of Maple throughout our courses. Animations are used in presentations in class from first year onwards. For example, animations for Newton’s method and for fixed point iteration; to illustrate how slicing is used to generate the domain for double integration; to show how the error function (for the collocation method solution of a boundary val...

Linear viscoelastic structures are characterized by dissipative forces that depend on the history of the velocity response via hereditary damping functions. The free motion equation leads to a nonlinear eigenvalue problem characterized by a frequency–dependent damping matrix. In the present paper, a novel and efficient numerical method for the computation of the eigenvalues of linear and propor...

Newton and quasi-Newton methods have been used in chemical process design and optimization calculations for quite some time. They continue to be used today, both in the traditional sense and as part of the more recent hybrid method. While Newton-based fixed-point methods have been used to solve many different kinds of chemical process design and optimization problems, perhaps the point of singl...

The following paper compares a consistent Newton-Raphson and fixed-point iteration based solution strategy for a variational multiscale finite element formulation for incompress-ible Navier–Stokes. The main contributions of this work include a consistent linearization of the Navier–Stokes equations, which provides an avenue for advanced algorithms that require origins in a consistent method. We...