A Basic Theorem in the Computation of Ellipsoidal Error Bounds.
A Galerkin method of for singular boundary value problems.
A posteriori error estimation for arbitrary order FEM applied to singularly perturbed one-dimensional reaction-diffusion problems
FEM discretizations of arbitrary order are considered for a singularly perturbed one-dimensional reaction-diffusion problem whose solution exhibits strong layers. A posteriori error bounds of interpolation type are derived in the maximum norm. An adaptive algorithm is devised to resolve the boundary layers. Numerical experiments complement our theoretical results.
A spectral regularization method for a Cauchy problem of the modified Helmholtz equation.
Accurate computation of higher Sturm-Liouville eigenvalues.
An algorithm for the numerical solution of differential equations of fractional order.
Asymptotic Error Estimation for One-Step Methods Based on Quadrature.
Computable error bounds for collocation methods.
Computable error bounds with improved applicability conditions for collocation methods.
Cubic spline difference scheme on a mesh of Bakhvalov type.
Defect correction and a posteriori error estimation of Petrov-Galerkin methods for nonlinear Volterra integro-differential equations
We present two defect correction schemes to accelerate the Petrov-Galerkin finite element methods [19] for nonlinear Volterra integro-differential equations. Using asymptotic expansions of the errors, we show that the defect correction schemes can yield higher order approximations to either the exact solution or its derivative. One of these schemes even does not impose any extra regularity requirement on the exact solution. As by-products, all of these higher order numerical methods can also be...
Error analysis of Adomian series solution to a class of nonlinear differential equations.
Error bounds for eigenvalues and eigenfunctions of some ordinary differential operators by the method of least squares
Error Bounds for the Solution of Nonlinear Two-point Boundary Value Problems by Galerkin's Method.
Error estimates and step-size control for the approximate solution of a first order evolution equation
Error estimates of a numerical method for a class of nonlinear evolution equations
Extensions of the HHT- method to differential-algebraic equations in mechanics.
Fractional-order Bessel functions with various applications
We introduce fractional-order Bessel functions (FBFs) to obtain an approximate solution for various kinds of differential equations. Our main aim is to consider the new functions based on Bessel polynomials to the fractional calculus. To calculate derivatives and integrals, we use Caputo fractional derivatives and Riemann-Liouville fractional integral definitions. Then, operational matrices of fractional-order derivatives and integration for FBFs are derived. Also, we discuss an error estimate between...
Frequency analysis of preconditioned waveform relaxation iterations
The error analysis of preconditioned waveform relaxation iterations for differential systems is presented. This analysis extends and refines previous results by Burrage, Jackiewicz, Nørsett and Renaut by incorporating all terms in the expansion of the error of waveform relaxation iterations in the Laplace transform domain. Lower bounds for the size of the window of rapid convergence are also obtained. The theory is illustrated for waveform relaxation methods applied to differential systems resulting...
Global error control for the continuous Galerkin finite element method for ordinary differential equations