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Systems of Vector Fields for the Integration of Ordinary Differential Equations
In this work, we investigate different classes of vector fields that can be used to find exact solutions of ordinary differential equations. The...
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Solutions
Only the component of the rain speed perpendicular to the surface contributes to the solution. Hence, in the previous solution, we just replace r by...
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On monodromy eigenfunctions of Heun equations and boundaries of phase-lock areas in a model of overdamped Josephson effect
We study a family of double confluent Heun equations of the form LE = 0, where L = L λ , μ , n is a family of second-order differential operators acting...
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On the convergence of multiple Richardson extrapolation combined with explicit Runge–Kutta methods
The order of accuracy of any convergent time integration method for systems of differential equations can be increased by using the sequence...
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On spectral asymptotic of quasi-exactly solvable quartic potential
Motivated by the earlier results of Masoero and De Benedetti (Nonlinearity 23:2501, 2010) and Shapiro et al. (Commun Math Phys 311(2):277–300, 2012),...
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Differential Equations
Differential equations provide a language for representing many processes in nature, technology, and society. Ordinary differential equations have...
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The Euler scheme for stochastic differential equations with discontinuous drift coefficient: a numerical study of the convergence rate
The Euler scheme is one of the standard schemes to obtain numerical approximations of solutions of stochastic differential equations (SDEs). Its...
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Numerische Verfahren, Mathematische Modelle
Numerische Methoden erlauben es, fast „beliebig“ komplizierte gewöhnliche Differentialgleichungen zu lösen und grafisch darzustellen. Mit ihnen hat...
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Difference Scheme with a Symmetry Analyzer for Equations of Magnetohydrodynamics
AbstractThe paper proposes a computational algorithm for the numerical simulation of two-dimensional magnetohydrodynamic (MHD) flows, using a...
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Calabi–Yau operators of degree two
We show that the solutions to the equations, defining the so-called Calabi–Yau condition for fourth-order operators of degree two, define a variety...
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Asymptotics of the Spectrum of the Hydrogen Atom in Orthogonal Electric and Magnetic Fields near the Lower Boundaries of Spectral Clusters
The Zeeman—Stark effect for the hydrogen atom in an electromagnetic field is considered by using irreducible representations of an algebra with...
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B-series and Runge–Kutta methods
The early Runge–Kutta methods were built around the aim of obtaining successively higher orders for a generic scalar problem. However, in modern...
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An implicit–explicit time discretization scheme for second-order semilinear wave equations with application to dynamic boundary conditions
We construct and analyze a second-order implicit–explicit (IMEX) scheme for the time integration of semilinear second-order wave equations. The...
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Solution of second kind Fredholm integral equations by means of Gauss and anti-Gauss quadrature rules
This paper is concerned with the numerical approximation of Fredholm integral equations of the second kind. A Nyström method based on the anti-Gauss...
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Quadratic differentials and signed measures
In this paper, motivated by the classical notion of a Strebel quadratic differential on a compact Riemann surface without boundary, we introduce...
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Numerical Methods with Applications
Numerical methods allow us to solve almost “arbitrarily complicated” ordinary differential equations and to graph the solution curves. They have the...
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Second Order Fully Semi-Lagrangian Discretizations of Advection-Diffusion-Reaction Systems
We propose a second order, fully semi-Lagrangian method for the numerical solution of systems of advection-diffusion-reaction equations, which is...
