Rapid variable-step computation of dynamic convolutions and Volterra-type integro-differential equations: RK45 Fehlberg, RK4
MN Azese - Heliyon, 2024 - cell.com
We introduce a novel, time-efficient adaptive Runge-Kutta computational scheme tailored for
systematically solving linear and nonlinear Volterra-type Integro-Differential Equations …
systematically solving linear and nonlinear Volterra-type Integro-Differential Equations …
Many-Stage Optimal Stabilized Runge–Kutta Methods for Hyperbolic Partial Differential Equations
A novel optimization procedure for the generation of stability polynomials of stabilized
explicit Runge–Kutta methods is devised. Intended for semidiscretizations of hyperbolic …
explicit Runge–Kutta methods is devised. Intended for semidiscretizations of hyperbolic …
NodePy: A package for the analysis of numerical ODE solvers
Ordinary differential equations (ODEs) are used to model a vast range of physical and other
phenomena. They also arise in the discretization of partial differential equations. In most …
phenomena. They also arise in the discretization of partial differential equations. In most …
Optimizing Linear/Non-linear Volterra-Type Integro-Differential Equations with Runge-Kutta 2 and 4 for Time Efficiency
MN Azese - Available at SSRN 4757395, 2024 - papers.ssrn.com
A novel time-efficient (TE) numerical scheme based on the Runge-Kutta (RK) algorithm is
devised for solving linear and non-linear Volterra-type integro-differential equations (VTIDE) …
devised for solving linear and non-linear Volterra-type integro-differential equations (VTIDE) …
Multirate Time-Integration based on Dynamic ODE Partitioning through Adaptively Refined Meshes for Compressible Fluid Dynamics
D Doehring, M Schlottke-Lakemper, GJ Gassner… - ar** schemes equipped with embedded error estimators, some of which …
Fourth-Order Paired-Explicit Runge-Kutta Methods
D Doehring, L Christmann… - arxiv preprint arxiv …, 2024 - arxiv.org
In this paper, we extend the Paired-Explicit Runge-Kutta schemes by Vermeire et. al. to
fourth-order of consistency. Based on the order conditions for partitioned Runge-Kutta …
fourth-order of consistency. Based on the order conditions for partitioned Runge-Kutta …
A class of high-order Runge–Kutta–Chebyshev stability polynomials
S O'Sullivan - Journal of Computational Physics, 2015 - Elsevier
The analytic form of a new class of factorized Runge–Kutta–Chebyshev (FRKC) stability
polynomials of arbitrary order N is presented. Roots of FRKC stability polynomials of degree …
polynomials of arbitrary order N is presented. Roots of FRKC stability polynomials of degree …
On the absolute stability regions corresponding to partial sums of the exponential function
Certain numerical methods for initial value problems have as stability function the nth partial
sum of the exponential function. We study the stability region, that is, the set in the complex …
sum of the exponential function. We study the stability region, that is, the set in the complex …
[PDF][PDF] Very High-Order A-stable Stiffly Accurate Diagonally Implicit Runge-Kutta Methods
Y Alamri, DI Ketcheson - 2022 - researchgate.net
A numerical search approach is used to design high-order diagonally implicit Runge-Kutta
(DIRK) schemes suitable for stiff and oscillatory systems. We present new A-stable schemes …
(DIRK) schemes suitable for stiff and oscillatory systems. We present new A-stable schemes …