Chebfun Solutions to a Class of 1D Singular and Nonlinear Boundary Value Problems
AbstractThe Chebyshev collocation method implemented in Chebfun is used in order to solve a class of second order one-dimensional singular…
Numerical Analysis
A new optimal method of order four of Hermite–Steffensen type
Abstract We introduce a new method for solving nonlinear equations in R, which uses three function evaluations at each step…
On high-order conforming finite element methods for ill-posed Helmholtz problems
Abstract We consider the numerical approximation of the linear ill-posed problem of unique continuation for the Helmholtz equation. We first…
Tikhonov regularization of a perturbed heavy ball system with vanishing damping
AbstractThis paper deals with aa perturbed heavy ball system with vanishing damping that contains a Tikhonov regularization term, in connection…
Global Random Walk Solutions for Flow and Transport in Porous Media
AbstractThis article presents a new approach to solve the equations of flow in heterogeneous porous media by using random walks…
Unique continuation problems and stabilised finite element methods
Book summaryNumerical analysis for partial differential equations (PDEs) traditionally considers problems that are well-posed in the continuum, for example the…
How many steps still left to x*?
We survey the convergence orders of sequences and show the orders of the basic iterative sequences for solving nonlinear equations…
Asymptotic analysis of a structure-preserving integrator for damped Hamiltonian systems
AbstractThe present work deals with the numerical long-time integration of damped Hamiltonian systems. The method that we analyze combines a…
Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media
AbstractIn this article, we present new random walk methods to solve flow and transport problems in saturated/unsaturated porous media, including coupled flow…
Accurate spectral collocation computations of high order eigenvalues for singular Schrödinger equations-revisited
AbstractIn this paper, we continue to solve as accurately as possible singular eigenvalues problems attached to the Schrödinger equation. We…