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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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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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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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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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On linearly implicit IMEX Runge-Kutta methods for degenerate convection-diffusion problems modeling polydisperse sedimentation
Implicit-explicit (IMEX) Runge-Kutta (RK) methods are suitable for the solution of nonlinear, possibly strongly degenerate, convection-diffusion...
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Convergence analysis of the formal energies of symplectic methods for Hamiltonian systems
Based on Feng’s theory of formal vector fields and formal flows, we study the convergence problem of the formal energies of symplectic methods for...
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Energy-conserving methods for Hamiltonian boundary value problems and applications in astrodynamics
We introduce new methods for the numerical solution of general Hamiltonian boundary value problems. The main feature of the new formulae is to...
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Bending of simply-supported circular timber beam strengthened with fiber reinforced polymer
The bending behavior of the circular cross-section timber beam strengthened with a fiber reinforced polymer (FRP) sheet is investigated. The tight...