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In this paper, we present an optimal fourth-order parameter-uniform non-monotone scheme on equidistributed meshes for singularly perturbed reaction–diffusion boundary value problems exhibiting boun...

In this paper, an asymmetric cryptosystem with unequal modulus decomposition in the Fourier domain is presented. The input-colour image is decomposed into its red, green, and blue components. Each ...

The current paper proposes a new high-order finite difference scheme with low computational complexity to solve the space-time fractional tempered diffusion equation. At the first stage, the time d...

The main aim of the current paper is to propose a new numerical scheme based on the Adams-Bashforth method for solving two component time fractional differential equations involving the Caputo-Prab...

Richardson's leapfrog scheme is notoriously unconditionally unstable in well-posed, forward, linear dissipative evolution equations. Remarkably, that scheme can be stabilized, marched backward in t...

We show existence of solution for a supercritical nonlinear Schrodinger equation on the whole RN by means of an approximation scheme. We prove a Sobolev embedding corresponding to the variable expo...

Motivated by computing medians and means, two proximal splitting methods, backward-backward scheme introduced by Passty [Ergodic convergence to a zero of the sum of monotone operators in Hilbert sp...

We propose a tamed-adaptive Euler-Maruyama approximation scheme for stochastic differential equations with locally Lipschitz continuous, polynomial growth drift, and locally Holder continuous, poly...

This paper discusses the point and interval estimation of two parameters of generalized inverted exponential distribution under the adaptive progressive type II hybrid censoring scheme. The maximum...

In this paper, the nonlinear Benjamin–Bona–Mahony–Burgers (BBMB) equation is solved using the septic Hermite collocation method (SHCM) for the space discretization and Crank–Nicholson scheme for th...

A three-level implicit difference scheme is developed for a inviscid Burgers' equation with time delay. It is proved that the proposed scheme is uniquely solvable, stable, and unconditionally conve...

In this paper, we consider one- and two-dimensional singularly perturbed parabolic reaction-diffusion problems. We propose a parameter-uniform numerical scheme to solve these problems. The continuo...

The aim of present study is to develop a numerical scheme by using the notion of Barycentric Lagrange interpolation based Differential quadrature method to solve the coupled 1D Burgers’ equation. T...

We present a fast and accurate numerical scheme for approximating weakly singular oscillatory Volterra integral equations (VIEs) of the second kind. The main idea is the combination of the black-bo...

In a companion paper, we present the theoretical development of a new robust, relaxation-free iteration scheme for multiphysics k-eigenvalue problems. These types of problems are essential to the s...

This paper presents a new robust scheme for coupled physics nuclear reactor calculations. We focus specifically on high-fidelity whole-core transport calculations with coarse mesh finite difference...

In this paper, we propose a new family of non-stationary subdivision scheme, based on mixed trigonometric hyperbolic B-spline basis functions with two tension and one shape parameters. We prove tha...

In this paper, an efficient finite difference scheme is proposed for one dimension and two dimension coupled space fractional nonlinear Schrodinger equations. First, the high-order difference schem...

We present a numerical scheme for the solution of two-parameter singularly perturbed problems whose solution has multi-scale behaviour in the sense that there are small regions where the solution c...

This paper continues the authors's study of robust numerical scheme for generalized Stein's model of neuronal variability, which is a singularly perturbed parabolic partial differential–difference ...

A new positivity-preserving finite volume scheme is proposed for solving the convection–diffusion equation on 2D or 3D distorted meshes. The nonlinear two-point flux approximation is applied to the...

In this paper, we investigate a numerical scheme for the singular Emden–Fowler problem using quintic B-spline. We eliminate the singularity of the problem according to Lopita's law and obtain a new...

Although weighted compact nonlinear scheme (WCNS) has been successfully applied to the simulation of complex configurations, due to the excessive dissipation, the scheme is still not suitable for m...

A nonlinear initial boundary value problem with a time Caputo derivative of fractional-order β∈(1,2) and a space Riesz derivative of fractional-order α∈(1,2) is considered. A linearized alternating...

The present study presents the application of a structural optimization scheme for a Double Split Hollow Sphere (DSHS) based acoustic cloaking structure for irregular surfaces. For acoustic wave cl...

In this article we introduce an inertial iterative scheme with self-adaptive step size for finding a common solution of split common null point problem for a finite family of maximal monotone opera...

In this paper we study the discrete approximation of backward stochastic differential equations. Under a kind of non-Lipschitz assumption we prove the convergence of the proposed discrete scheme to...

In this paper, we first introduce the concept of the convex graphical rectangular b-metric space ( GRbCMS) by means of the convex structure. Moreover, the definitions of G-contraction mappings, G-q...

A total variation bounded (TVB) Runge–Kutta local-projection discontinuous Galerkin (RK-LDG) finite element method is applied for numerically approximating the non-isothermal and non-equilibrium mo...

In this study, analytical expressions are developed for average symbol error rate (ASER) of rectangular quadrature amplitude modulation (RQAM) scheme over α−μfading channels. Initially, the ASER ex...

Cellular structures (CSs) exhibit unique combinations of physical properties, including low weight, high structural strength, and substantial energy absorption, which could be useful in a variety o...

This paper analyzes a two-level factored implicit scheme in a numerical solution of two-dimensional unsteady advection-diffusion equation with time dependent dispersion coefficients subjects to ini...

In this paper, we aim to build confidence regions of the true solution to the stochastic variational inequalities problem (SVIP) when the sample average approximation (SAA) scheme is implemented. A...

This paper applies an explicit numerical method, i.e. the truncated Euler–Maruyama (EM) scheme, to investigate numerical approximations for nonlinear and non-autonomous stochastic differential equa...

In this article, a meshfree spectral interpolation technique combined with Crank–Nicolson difference scheme is proposed to solve a class of strongly non-linear Burgers–Fisher type equation numerica...

We consider the problem of minimizing a finite sum of convex functions subject to the set of minimizers of a convex differentiable function. In order to solve the problem, an algorithm combining the incremental proximal gradient method with smooth penalization technique is proposed. We show the convergence of the generated sequence of iterates to an optimal solution of the optimization problems, provided that a condition expressed via the Fenchel conjugate of the constraint function is fulfilled. Finally, the functionality of the method is illustrated by some numerical experiments addressing image inpainting problems and generalized Heron problems with least squares constraints.

Recently, a threshold d − level quantum secret sharing scheme was presented by Song et al. However, Kao et al. showed that in contrary to Song claim, the reconstructor cannot recover the secret wit...

A class of singularly perturbed parabolic delay differential equation with discontinuous data is solved numerically. Numerical scheme based on the upwind finite difference method is presented on a ...

In this work, we describe a numerical scheme based on modified moving least-square (MMLS) method for solving Fredholm–Hammerstein integral equations on 2D irregular domains. The moment matrix in mo...

In this paper, we present a two-grid scheme of expanded mixed finite element method combined with two second-order time discretization schemes for semilinear parabolic integro-differential equation...

In this paper, an efficient semi-implicit difference scheme for solving the fractional nonlinear Schrodinger equation with wave operator are proposed and analyzed. The semi-implicit scheme involves...

In this paper, a high-accuracy conservative difference scheme is presented for solving the space fractional Zakharov system, which preserves the original conservative properties. By virtue of the s...

This paper develops and analyses a finite difference/spectral-Galerkin scheme for the nonlinear fractional Schrodinger equations with Riesz space- and Caputo time-fractional derivatives. The L 1 fi...

This paper develops a new hybrid finite difference scheme which consists of a nonlinear WENOCU4 scheme to maintain the numerical stability near discontinuities and a fourth-order linear central sche...

We consider the generalized Burgers–Huxley (GBH) equation subject to certain initial and boundary conditions (BCs). Using a solitary wave solution, we derive an exact finite difference (EFD) scheme...

The implicit Monte Carlo (IMC) method can exhibit teleportation error in problems with strong coupling between radiation and material. Source tilting method is a technique to reduce the teleportati...

Based on the non-alternating preconditioned HSS iteration scheme, a class of the Uzawa-NPHSS iteration method for solving nonsingular and singular non-Hermitian saddle point problems with the (1,1)...

It is generally known that explicit solution can rarely be obtained for stochastic differential equations (SDEs), not to mention the nonlinear stochastic functional differential equation (SFDEs). T...

This work presents a partitioned solution procedure to compute shape gradients in fluid-structure interaction (FSI) using black-box adjoint solvers. Special attention is paid to project the gradients onto the undeformed configuration. This is due to the mixed Lagrangian-Eulerian formulation of large-displacement FSI in this work. Adjoint FSI problem is partitioned as an assembly of well-known adjoint fluid and structural problems, without requiring expensive cross-derivatives. The sub-adjoint problems are coupled with each other by augmenting the target functions with auxiliary functions, independent of the concrete choice of the underlying adjoint formulations. The auxiliary functions are linear force-based or displacement-based functionals which are readily available in well-established single-disciplinary adjoint solvers. Adjoint structural displacements, adjoint fluid displacements, and domain-based adjoint sensitivities of the fluid are the coupling fields to be exchanged between the adjoint solvers. A reduced formulation is also derived for the case of boundary-based adjoint shape sensitivity analysis for fluids. Numerical studies show that the complete formulation computes accurate shape gradients whereas inaccuracies appear in the reduced gradients, specially in regions of strong flow gradients and near singularities. Nevertheless, reduced gradient formulations are found to be a compromise between computational costs and accuracy. Mapping techniques including nearest element interpolation and the mortar method are studied in computational adjoint FSI. It is numerically shown that the mortar method does not introduce spurious oscillations in primal and sensitivity fields along non-matching interfaces, unlike the nearest element interpolation.

We consider a multidimensional system of hyperbolic equations with fractional diffusion, constant damping and nonlinear reactions. The system considers fractional Riesz derivatives, and generalizes...