We develop a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In the one dimensional case that we consider here, our methods require only C3 regularity of the maps in the IFS. The key idea, which has been known in varying degrees of generality for many years, is to associate to the IFS a parametrized family of positive, linea...

This paper proposes a novel adaptive higher-order finite element (hp-FEM) method for solving elliptic eigenvalue problems, where n eigenpairs are calculated simultaneously, but on individual meshes. The meshes automatically hp-refined independently of each other, with the goal to use an optimal mesh sequence eigenfunction. and algorithm described in detail. Numerical examples clearly demonstrat...

The Wright-Fisher family of diffusion processes is a class of evolutionary models widely used in population genetics, with applications also in finance and Bayesian statistics. Simulation and inference from these diffusions is therefore of widespread interest. However, simulating a Wright-Fisher diffusion is difficult because there is no known closed-form formula for its transition function. In...

The Moving Finite Element method for the solution of time-dependent partial diierential equations is a numerical solution scheme which allows the automatic adaption of the nite element approximation space with time, through the use of mesh relocation (r-reenement). This paper analyses the asymptotic behaviour of the method for large times when it is applied to the solution of a class of self-ad...

The use of numerical tools to solve challenging problems in mathematics has exploded in the past several decades. The purpose of this paper is to compare the results of two different types of numerical methods in finding solutions to the eigenvalue problem for a second-order elliptic differential equation subject to boundary and transmission conditions. The transmission conditions result from j...

The Moving Finite Element method for the solution of time-dependent partial dierential equations is a numerical solution scheme which allows the automatic adaption of the nite element approximation space with time, through the use of mesh relocation (r-renement). This paper analyses the asymptotic behaviour of the method for large times when it is applied to the solution of a class of self-adjo...

This paper develops an averaging technique based on the combination of eigenfunction expansion method and collaboration to investigate multiple scattering effect SH wave propagation in a porous medium. The semi-analytical is conducted using Monto Carlo understand macroscopic dispersion attenuation phenomena stress solid due effects. verified by finite element analysis. Finally, simple homogeniz...

Abstract: In this paper, a perturbing nonlinear homogeneous Schrodinger equation is studied under limited time interval, complex initial conditions and zero Neumann conditions. The perturbation and Picard approximation methods together with the eigenfunction expansion and variational parameters methods are used to introduce an approximate solution for the perturbative nonlinear case for which a...

Perron-Frobenius operators and their eigendecompositions are increasingly being used as tools of global analysis for higher dimensional systems. The numerical computation of large, isolated eigenvalues and their corresponding eigenfunctions can reveal important persistent structures such as almostinvariant sets, however, often little can be said rigorously about such calculations. We attempt to...

We present a computational method for solving a class of boundary-value problems in Sturm-Liouville form. The algorithms are based on global polynomial collocation methods and produce discrete representations of the eigenfunctions. Error control is performed by evaluating the eigenvalue problem residuals generated when the eigenfunctions are interpolated to a finer discretization grid; eigenfun...