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IMEX-RK Finite Volume Methods for Nonlinear 1d Parabolic PDEs. Application to Option Pricing
The goal of this paper is to develop 2nd order Implicit-Explicit Runge-Kutta (IMEX-RK) finite volume (FV) schemes for solving 1d parabolic PDEs for...
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High Order Asymptotic Preserving and Classical Semi-implicit RK Schemes for the Euler–Poisson System in the Quasineutral Limit
In this paper, the design and analysis of high order accurate IMEX finite volume schemes for the compressible Euler–Poisson (EP) equations in the...
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Split S-ROCK Methods for High-Dimensional Stochastic Differential Equations
We propose explicit stochastic Runge–Kutta (RK) methods for high-dimensional Itô stochastic differential equations. By providing a linear error...
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Spectral Analysis of High Order Continuous FEM for Hyperbolic PDEs on Triangular Meshes: Influence of Approximation, Stabilization, and Time-Step**
In this work we study various continuous finite element discretization for two dimensional hyperbolic partial differential equations, varying the...
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Multiple-Relaxation Runge Kutta Methods for Conservative Dynamical Systems
We generalize the idea of relaxation time step** methods in order to preserve multiple nonlinear conserved quantities of a dynamical system by...
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Well-Balanced Methods for Compressible Euler Equations with Gravitational Force that Preserve Transonic Stationary Solutions
In some previous works, the authors introduced a general methodology to design high-order well-balanced finite-volume methods for one-dimensional...
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Spectral Analysis of Continuous FEM for Hyperbolic PDEs: Influence of Approximation, Stabilization, and Time-Step**
We study continuous finite element dicretizations for one dimensional hyperbolic partial differential equations. The main contribution of the paper...
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Continuous–Time Deterministic Systems
We now consider a deterministic continuous–time optimal control problem (OCP)Optimal control problem (OCP)continuous–time in which the state process...
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Runge-Kutta Methods
Order barriers of linear multistep methods are rather severe. In this chapter, we move to a different family of methods, i.e., Runge-Kutta methods,...
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Multivalue Methods
Previous chapters have analyzed numerical methods for ODEs according to multistep or multistage strategies, by linear multistep and Runge-Kutta...
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Continuous-Time Inverse Optimal Control
In this chapter, we investigate inverse optimal control problems for continuous-time dynamical systems governed by ordinary differential equations....
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Continuous stage stochastic Runge–Kutta methods
In this work, a version of continuous stage stochastic Runge–Kutta (CSSRK) methods is developed for stochastic differential equations (SDEs). First,...
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Runge–Kutta Methods for ODEs
Since an analytically-closed form solution of ordinary differential equations (ODEs) is hardly possible in real-world applications, their numerical...
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Stage-based interpolation Runge–Kutta methods for nonlinear Volterra functional differential equations
In this paper we study stability and convergence of stage-based interpolation Runge–Kutta (SBIRK) methods in which the functional term is...
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Legendre Superconvergent Degenerate Kernel and Nyström Methods for Nonlinear Integral Equations
We study polynomially based superconvergent collocation methods for the approximation of solutions to nonlinear integral equations. The...
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Stochastic modeling of stationary scalar Gaussian processes in continuous time from autocorrelation data
We consider the problem of constructing a vector-valued linear Markov process in continuous time, such that its first coordinate is in good agreement...
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Discontinuous Galerkin and Related Methods for ODE
A defining feature of the discontinuous Galerkin (DG) method for ODE is that the piecewise polynomial solution can have a jump discontinuity at the...
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Discrete Adjoint Computations for Relaxation Runge–Kutta Methods
Relaxation Runge–Kutta methods reproduce a fully discrete dissipation (or conservation) of entropy for entropy stable semi-discretizations of...
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Runge–Kutta–Möbius methods
In the numerical integration of nonlinear autonomous initial value problems, the computational process depends on the step size scaled vector field hf ...
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Asymptotical Stability of Neutral Reaction-Diffusion Equations with PCAS and Their Finite Element Methods
This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous...