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On the properties of the exceptional set for the randomized Euler and Runge-Kutta schemes
We show that the probability of the exceptional set decays exponentially for a broad class of randomized algorithms approximating solutions of ODEs,...
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An alternative approach for order conditions of Runge-Kutta-Nyström methods
We present an alternative approach proposed by Albrecht to derive general order conditions for Runge-Kutta-Nyström methods and relate it to the...
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Arbitrary high-order structure-preserving methods for the quantum Zakharov system
In this paper, we present a new methodology to develop arbitrary high-order structure-preserving methods for solving the quantum Zakharov system. The...
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A new framework for polynomial approximation to differential equations
In this paper, we discuss a framework for the polynomial approximation to the solution of initial value problems for differential equations. The...
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On the maximum principle and high-order, delay-free integrators for the viscous Cahn–Hilliard equation
The stabilization approach has been known to permit large time-step sizes while maintaining stability. However, it may “slow down the convergence...
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Stability and error estimates for the variable step-size BDF2 method for linear and semilinear parabolic equations
In this paper, stability and error estimates for time discretizations of linear and semilinear parabolic equations by the two-step backward...
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Numerical modelling of generalized Newtonian fluids in bypass tube
The following paper describes a numerical simulation of a complete bypass of a stenosed human artery. The considered geometry consists of the...
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Optimal convergence orders of fully geometric mesh one-leg methods for neutral differential equations with vanishing variable delay
The purpose of this paper is to obtain the error bounds of fully geometric mesh one-leg methods for solving the nonlinear neutral functional...
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Entropy generation analysis of natural convective radiative second grade nanofluid flow between parallel plates in a porous medium
The present article explores the entropy generation of radiating viscoelastic second grade nanofluid in a porous channel confined between two...
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Efficient Energy-preserving Methods for General Nonlinear Oscillatory Hamiltonian System
In this paper, we propose and analyze two kinds of novel and symmetric energy-preserving formulae for the nonlinear oscillatory Hamiltonian system of...
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Explicit Gautschi-type integrators for nonlinear multi-frequency oscillatory second-order initial value problems
The main theme of this paper is explicit Gautschi-type integrators for the nonlinear multi-frequency oscillatory second-order initial value problems...
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Trigonometric-Fitted Explicit Numerov-Type Method with Vanishing Phase-Lag and Its First and Second Derivatives
An effectively four-stage, sixth-order, hybrid explicit Numerov-type method is presented for the solution of the special second-order initial value...
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Stability of Numerical Solutions for Abel–Volterra Integral Equations of the Second Kind
We analyze the stability of convolution quadrature methods for weakly singular Volterra integral equations with respect to a linear test equation. We...
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Convergence of discrete time waveform relaxation methods
This paper concerns the discrete time waveform relaxation (DWR) methods for ordinary differential equations (ODEs). We present a general algorithm of...
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On Ninth Order, Explicit Numerov-Type Methods with Constant Coefficients
A new family of effectively nine stages, ninth-order hybrid explicit Numerov-type methods is presented for the solution of some special second order...
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A new class of efficient one-step contractivity preserving high-order time discretization methods of order 5 to 14
A family of one-step, explicit, contractivity preserving, multi-stage, multi-derivative, Hermite–Birkhoff–Taylor methods of order p = 5,6,…,14, that...
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On FBDF5 Method for Delay Differential Equations of Fractional Order with Periodic and Anti-Periodic Conditions
In this paper, we study the fractional backward differential formula (FBDF) for the numerical solution of fractional delay differential equations...
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Extended phase properties and stability analysis of RKN-type integrators for solving general oscillatory second-order initial value problems
In this paper, we study in detail the phase properties and stability of numerical methods for general oscillatory second-order initial value problems...
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A feasible and effective technique in constructing ERKN methods for multi-frequency multidimensional oscillators in scientific computation
In last few years, many ERKN methods have been investigated for solving multi-frequency multidimensional second-order ordinary differential...