54 citations · 65 across the 6 of their papers we have counts for
10 papers
Optimized linear multistep methods for stiff problems
Tyler Jensen, David I Ketcheson, Lajos Lóczi
We design and test several new optimized linear multistep methods for stiff problems. Each method is A-stable, implicit, and second-order accurate. We focus on achieving the smalle…
Explicit and recursive estimates of the Lambert W function
Lajos Lóczi
Solutions to a wide variety of transcendental equations can be expressed in terms of the Lambert function. The function, occurring frequently in applicati…
General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes
Hendrik Ranocha, Lajos Lóczi, David I. Ketcheson
Recently, an approach known as relaxation has been developed for preserving the correct evolution of a functional in the numerical solution of initial-value problems, using Runge-K…
Optimal subsets in the stability regions of multistep methods
Lajos Lóczi
In this work we study the stability regions of linear multistep or multiderivative multistep methods for initial-value problems by using techniques that are straightforward to impl…
Positivity for convective semi-discretizations
Imre Fekete, David I. Ketcheson, Lajos Lóczi
We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to…
Exact optimal values of step-size coefficients for boundedness of linear multistep methods
Lajos Lóczi
Linear multistep methods (LMMs) applied to approximate the solution of initial value problems---typically arising from method-of-lines semidiscretizations of partial differential e…
Dense output for strong stability preserving Runge-Kutta methods
David I. Ketcheson, Lajos Lóczi, Aliya Jangabylova +1
We investigate dense output formulae (also known as continuous extensions) for strong stability preserving (SSP) Runge-Kutta methods. We require that the dense output formula also…
Strong stability preserving explicit linear multistep methods with variable step size
Yiannis Hadjimichael, David Ketcheson, Lajos Lóczi +1
Strong stability preserving (SSP) methods are designed primarily for time integration of nonlinear hyperbolic PDEs, for which the permissible SSP step size varies from one step to…
Discretizing the transcritical and pitchfork bifurcations -- conjugacy results
Lajos Lóczi
We present two case studies in one-dimensional dynamics concerning the discretization of transcritical (TC) and pitchfork (PF) bifurcations. In the vicinity of a TC or PF bifurcati…
Rational functions with maximal radius of absolute monotonicity
Lajos Loczi, David I. Ketcheson
We study the radius of absolute monotonicity R of rational functions with numerator and denominator of degree s that approximate the exponential function to order p. Such functions…