Gaussian quadrature rules and A‐stability of Galerkin schemes for ODE
The A‐stability properties of continuous and discontinuous Galerkin methods for solving ordinary differential equations (ODEs) are established using properties of Legendre polynomials and Gaussian quadrature rules. The influence on the A‐stability of the numerical integration using Gaussian quadrature rules involving a parameter is analyzed.
Ali Bensebah+2 more
wiley +1 more source
Iterative solution of unstable variational inequalities on approximately given sets
The convergence and the stability of the iterative regularization method for solving variational inequalities with bounded nonsmooth properly monotone (i.e., degenerate) operators in Banach spaces are studied. All the items of the inequality (i.e., the operator A, the “right hand side” f and the set of constraints Ω) are to be perturbed. The connection
Y. I. Alber, A. G. Kartsatos, E. Litsyn
wiley +1 more source
Numerical Analysis of Transmission Lines Equation by new β-method Schemes
In this paper we develop a new β-method applied to the resolution of homogeneous transmission lines. A comparison with conventional methods used for this type of problems like FDTD method or classical β-method is also given.
Allali Fatima+3 more
doaj +1 more source
DIRK Schemes with High Weak Stage Order
Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems.
A Ditkowski+9 more
core +1 more source
Almost sure exponential stability of numerical solutions for stochastic delay differential equations [PDF]
Using techniques based on the continuous and discrete semimartingale convergence theorems, this paper investigates if numerical methods may reproduce the almost sure exponential stability of the exact solutions to stochastic delay differential equations (
A. Rodkina+28 more
core +1 more source
Runge-Kutta-Gegenbauer explicit methods for advection-diffusion problems [PDF]
In this paper, Runge-Kutta-Gegenbauer (RKG) stability polynomials of arbitrarily high order of accuracy are introduced in closed form. The stability domain of RKG polynomials extends in the the real direction with the square of polynomial degree, and in ...
O'Sullivan, Stephen
core +3 more sources
Strong convergence rates for backward Euler–Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients [PDF]
In this work, we generalize the current theory of strong convergence rates for the backward Euler–Maruyama scheme for highly non-linear stochastic differential equations, which appear in both mathematical finance and bio-mathematics.
Mao, Xuerong, Szpruch, Lukasz
core +1 more source
Almost sure exponential stability of the Euler–Maruyama approximations for stochastic functional differential equations [PDF]
By the continuous and discrete nonnegative semimartingale convergence theorems, this paper investigates conditions under which the Euler–Maruyama (EM) approximations of stochastic functional differential equations (SFDEs) can share the almost sure ...
Kloeden, Peter E.+2 more
core +1 more source
A posteriori error estimates for mixed finite volume solution of elliptic boundary value problems
The major emphasis of this work is the derivation of a posteriori error estimates for the mixed finite volume discretization of second-order elliptic equations. The estimates are established for meshes consisting of simplices on unstructured grids.
Benkhaldoun Fayssal+2 more
doaj +1 more source
Sharp eigenvalue enclosures for the perturbed angular Kerr-Newman Dirac operator [PDF]
A certified strategy for determining sharp intervals of enclosure for the eigenvalues of matrix differential operators with singular coefficients is examined.
Boulton L+5 more
core +3 more sources