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Non-Oscillatory Central Schemes for the Incompressible 2D Euler Equations
Hyperbolic conservation laws second-order accuracy central difference schemes non-oscillatory schemes Incompressible Euler equations
2015/10/8
We adopt a non-oscillatory central scheme, first presented in the context of Hyperbolic conservation laws in [nessyahu-tadmor] followed by [jiang-tadmor], to the framework of the incompressible Eule...
INVISCID MODELS GENERALIZING THE 2D EULER AND THE SURFACE QUASI-GEOSTROPHIC EQUATIONS
INVISCID MODELS GENERALIZING 2D EULER THE SURFACE QUASI-GEOSTROPHIC EQUATIONS
2014/4/3
Any classical solution of the 2D incompressible Euler equation is global in time. However, it remains an outstanding open problem whether classical solutions of the surface quasi-geostrophic (SQG) equ...
Feynman Formulas Representation of Semigroups Generated by Parabolic Difference-Differential Equations
Difference-Differential Equations Semigroup Feynman Formula Chernoff Theorem
2013/1/30
We establish that the Laplas operator with perturbation by symmetrised linear hall of displacement argument operators is the generator of unitary group in the Hilbert space of square integrable functi...
Nonconforming H1-Galerkin Mixed Finite Element Method for Pseudo-Hyperbolic Equations
Pseudo-Hyperbolic Equation Nonconforming H1-Galerkin Mixed Finite Element Error Estimate
2013/1/30
Based on H1-Galerkin mixed finite element method with nonconforming quasi-Wilson element, a numerical approximate scheme is established for pseudo-hyperbolic equations under arbitrary quadrilateral me...
Recent Modifications of Adomian Decomposition Method for Initial Value Problem in Ordinary Differential Equations
Adomian Decomposition Method Initial Value Problem Modified Adomian Decomposition Method
2013/1/30
In this paper, some modifications of Adomian decomposition method are presented for solving initial value problems in ordinary differential equations. Also, the restarted and two-step methods are appl...
Some Examples to Show that Objects be Presented by Mathematical Equations
Graph, Equation Visible and Invisible Object
2013/1/30
We have often heard remarks such as “We can plot graphs from the mathematical equations”, including equations of lines, equations of curves, and equations of invisible and visible objects. Actually, w...
Multilevel Correction For Collocation Solutions of Volterra Integral Equations With Proportional Delays
delay integral equation geometric mesh collocation method superconvergence
2012/8/10
In this paper we propose a convergence acceleration method
for collocation solutions of the linear second-kind Volterra integral
equations with proportional delay qt (0 < q < 1). This convergence
a...
Boundary Value Problems for Differential Equations of Fractional Order
Boundary Value Problems Fractional Order
2012/8/10
We carry out spectral analysis of one class of integral op-
erators associated with fractional order differential equations that arise in
mechanics. We establish a connection between the eigenvalues...
Solving Two-Point Boundary Value Problems of Fractional Differential Equations by Spline Collocation Methods
Caputo抯 derivatives Collocation methods Cubic spline functions Riemann-Liouvillefractional derivative
2012/8/10
We use collocation methods to solve fractional boundary value problems. Analytically, we study the
existence and uniquenes theorem of the collocation solutions, and discuss some error estimates. We
...
Solving Two-Point Boundary Value Problems of Fractional Differential Equations
Caputo抯 derivatives Riemann-Liouville Derivatives Fractional differential equation Twopointboundary value problem Existence and uniqueness Single shooting method
2012/8/8
We solve four kinds of two-point boundary value problems of fractional differential equations with
Caputo抯 derivatives or Riemann-Liouville Derivatives. Analytically, we introduce the fractional Gree...
G1 B-Spline Surface Construction By Geometric Partial Differential Equations
B-Spline surface discretizations geometric PDE Convergence
2012/8/8
In this paper, we propose a dynamic B-spline technique using general form fourth order geometric
PDEs. Basing on discretizaions of Laplace-Beltrami operator and Gaussian curvature over triangular
an...
G1 Spline Surface Construction By Geometric Partial Differential Equations Using Mixed Finite Element Methods
Spline surface Discretizations GPDE Convergence
2012/8/8
Variational formulations of three fourth order geometric partial di甧rential equations are
derived, and based on which mixed 痭ite element methods are presented for constructing
G1 smooth B-spline sur...
Symplectic Discretization for Spectral Element Solution of Maxwell’s Equations
Maxwell’s Equations Spectral Element Method Poisson System Sym-plectic Partitioned Runge-Kutta Method
2012/8/8
Based on the GLL-spectral element discretization of time-dependent Maxwell’s equa-
tions introduced recently, we obtain a Poisson system or a Poisson system with a little
oscillation. We prove that ...
An Adaptive Multilevel Method For Time-Harmonic Maxwell Equations With Singularities
Maxwell's equations singularities of solutions adaptive 痭 ite element method multigrid method
2012/8/8
We develop an adaptive edge 痭ite element method based on reliable and e眂ient
residual-based a posteriori error estimates for low-frequency time-harmonic Maxwell's equations with
singularities. The r...
Classical Conservative Properties of Five Difference Schemes for Coupled Klein-Gordon-Schr ?dinger Equations
Klein-Gordon-Schr膐dinger equations difference schemes conservation
2012/8/7
In this paper we compare the classical conservative properties of 痸e
di甧rence schemes applied to the coupled Klein-Gordon-Schr膐dinger equations in the
quantum physics, and investigate the numerical ...