Fifth-order numerical methods for heat equation subject to a boundary integral specification.
Fifth-order Runge-Kutta with higher order derivative approximations.
Finite Difference Methods and Their Convergence for a Class of Singular Two Point Boundary Value Problems.
Finite difference methods for computing eigenvalues of fourth order boundary value problems.
Finite-difference method for parameterized singularly perturbed problem.
Finite-time outer synchronization between two complex dynamical networks with time delay and noise perturbation
In this paper, the finite-time stochastic outer synchronization and generalized outer synchronization between two complex dynamic networks with time delay and noise perturbation are studied. Based on the finite-time stability theory, sufficient conditions for the finite-time outer synchronization are obtained. Numerical examples are examined to illustrate the effectiveness of the analytical results. The effect of time delay and noise perturbation on the convergence time are also numerically demonstrated....
First and third boundary value problems for the equation of the second order with non-continuous coefficients
Formal adjoints of linear DAE operators and their role in optimal control.
Former super-irrécductibles des systèmes différentiels linéaires.
Fourth order time-stepping for low dispersion Korteweg-de Vries and nonlinear Schrödinger equations.
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...
From the theorem of Ważewski to computer assisted proofs in dynamics
Fully discrete error estimation by the method of lines for a nonlinear parabolic problem
A posteriori error estimates for a nonlinear parabolic problem are introduced. A fully discrete scheme is studied. The space discretization is based on a concept of hierarchical finite element basis functions. The time discretization is done using singly implicit Runge-Kutta method (SIRK). The convergence of the effectivity index is proven.
Galerkin Approximations for the Two Point Boundary Problem Using Continuous, Piecewise Polynomial Spaces.
Galerkin-wavelet methods for two-point boundary value problems.
Gaussian collocation via defect correction.
Gaussian quadrature rules and -stability of Galerkin schemes for ODE.
General Framework, Stability and Error Analysis for Numerical Stiff Boundary Value Methods.
General linear methods: connection to one step methods and invariant curves.