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Uniformly Accurate Nested Picard Iterative Integrators for the Klein-Gordon Equation in the Nonrelativistic Regime
In this paper, a class of uniformly accurate nested Picard iterative integrator (NPI) Fourier pseudospectral methods is proposed for the nonlinear...
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Uniformly accurate nested Picard integrators for a system of oscillatory ordinary differential equations
A uniformly second order accurate nested Picard iterative integrator (NPI) is proposed to solve a system of oscillatory ordinary equations involving...
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On numerical methods for the semi-nonrelativistic limit system of the nonlinear Dirac equation
Solving the nonlinear Dirac equation in the nonrelativistic limit regime numerically is difficult, because the solution oscillates in time with...
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Multirate Schemes — An Answer of Numerical Analysis to a Demand from Applications
In science and engineering, simulation tasks often involve numerical time integration of differential equations. Usually, these systems contain...
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An Exactly Curl-Free Staggered Semi-Implicit Finite Volume Scheme for a First Order Hyperbolic Model of Viscous Two-Phase Flows with Surface Tension
In this paper, we present a pressure-based semi-implicit numerical scheme for a first order hyperbolic formulation of compressible two-phase flow...
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Models in Two-Dimensions
In this chapter we describe how to implement geophysical fluid dynamics models in Firedrake, focusing on two-dimensional models. The chapter is...
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Computational Aspects of Some Exponential Identities
The notion of the exponential of a matrix is usually introduced in elementary textbooks on ordinary differential equations when solving a constant...
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Faster SDC convergence on non-equidistant grids by DIRK sweeps
Spectral deferred correction methods for solving stiff ODEs are known to converge reasonably fast towards the collocation limit solution on...
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Direct Optimization: Problem discretization
The goal of this chapter is to obtain a discretized version of OCP (2.6). We discuss a so-called direct approach and summarize its main advantages...
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Quadrature methods for highly oscillatory linear and non-linear systems of ordinary differential equations: part II
In this paper we present efficient numerical approximation for systems of highly oscillatory ordinary differential equations with matrices of...
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A Newton-Picard Collocation Method for Periodic Solutions of Delay Differential Equations
This paper presents a collocation method with an iterative linear system solver to compute periodic solutions of a system of autonomous delay...
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Rough functions: p-Variation, calculus, and index estimation
In this paper, we give an overview of several dissipated results on the p -variation property of a function presented in a suitable way. More...
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Stochastic Processes in Continuous Time
The underlying set-up is as in Chapter 3: we need a complete probability space (Ω, F, ℙ), equipped with a filtration, i.e a nondecreasing family...
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Multiscale Concepts for Moving Horizon Optimization
In chemical engineering complex dynamic optimization problems formulated on moving horizons have to be solved on-line. In this work, we present a...
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Efficient Parallel Computation of Periodic Solutions of Parabolic Partial Differential Equations
Periodic solutions of autonomous parabolic partial differential systems can be computed by using a shooting method, applied to the (large) system of...