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Explicit MPC Solution Using Hasse Diagrams: Construction, Storage and Retrieval
This chapter provides new methods for the construction, storage and retrieval of the explicit MPC solution in the case with quadratic cost and linear...
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On the Maxwell-wave equation coupling problem and its explicit finite-element solution
It is well known that in the case of constant dielectric permittivity and magnetic permeability, the electric field solving the Maxwell’s equations...
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Asymptotics of the Solution of an Initial–Boundary Value Problem for the One-Dimensional Klein–Gordon Equation on the Half-Line
AbstractThe initial–boundary value problem for the Klein–Gordon equation on the half-line is considered. It is possible to reduce to this problem...
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Semi-implicit methods for advection equations with explicit forms of numerical solution
We present a parametric family of semi-implicit second order accurate numerical methods for non-conservative and conservative advection equation for...
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One-Dimensional Variational Problems
This chapter is devoted to one of the most classical classes of variational problems, the one-dimensional case.
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On Solutions of the One-Dimensional Goldshtik Problem
AbstractA one-dimensional analog of the Goldshtik mathematical model for separated flows in an incompressible fluid is considered. The model is a...
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Singly TASE Operators for the Numerical Solution of Stiff Differential Equations by Explicit Runge–Kutta Schemes
In this paper new explicit integrators for numerical solution of stiff evolution equations are proposed. As shown by Bassenne, Fu and Mani in (J...
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The Calculus of Variations for One-dimensional Problems
The goal of this chapter is to study one-dimensional variational problems where one tries to minimize an integral functionalIntegral functional of...
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Scattering Problem of Three One-Dimensional Quantum Particles. Case of Repulsive Coulomb Pair Potentials at Large Distances
The present paper considers the quantum scattering problem for three one-dimensional particles with pair Coulomb repulsion potentials at large...
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Solutions with moving singularities for a one-dimensional nonlinear diffusion equation
The aim of this paper is to study singular solutions for a one-dimensional nonlinear diffusion equation. Due to slow diffusion near singular points,...
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One-Dimensional Stochastic Equations
In this chapter we establish several stochastic equations for one-dimensional CBIprocesses. By considering a particular stochastic equation, we...
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Numerical Analysis of the Blow-Up of One-Dimensional Polymer Fluid Flow with a Front
AbstractOne-dimensional flows of an incompressible viscoelastic polymer fluid that are qualitatively similar to the solutions of Burgers’ equation...
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The High-Order Variable-Coefficient Explicit-Implicit-Null Method for Diffusion and Dispersion Equations
For the high-order diffusion and dispersion equations, the general practice of the explicit-implicit-null (EIN) method is to add and subtract an...
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Statistical and transport properties of a one-dimensional random walk with periodically distributed trap** intervals
Following the kind invitation of the organizers of the Fourth DinAmicI Day, I gave on December, 17, 2021, a talk concerning the study of a random...
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Sharp Interface Limit for the One-dimensional Compressible Navier-Stokes/Allen-Cahn System with Composite Waves
This paper is concerned with the sharp interface limit of Cauchy problem for the one-dimensional compressible Navier-Stokes/Allen-Cahn system with a...
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Ritz-type projectors with boundary interpolation properties and explicit spline error estimates
In this paper we construct Ritz-type projectors with boundary interpolation properties in finite dimensional subspaces of the usual Sobolev space and...
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One-Dimensional Finite-Gap Schrödinger Operators As a Limit of Commuting Difference Operators
AbstractIn this paper we show that the one-dimensional finite-gap Schrödinger operator can be obtained via passage to the limit from a second-order...
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Gap Labelling for Discrete One-Dimensional Ergodic Schrödinger Operators
In this survey, we give an introduction to and proof of the gap labelling theorem for discrete one-dimensional ergodic Schrödinger operators via the...
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On Expansions in the Exact and Asymptotic Eigenfunctions of the One-Dimensional Schrödinger Operator
AbstractThe one-dimensional Schrödinger operator with potential growing at infinity and with a semiclassical small parameter is considered. We...