The general quasi-linear autonomous fourth order diffusion equation ut = −[G(u)uxxx + h(u, ux, uxx)]x with positive variable diffusivity G(u) and lower-order flux component h is considered on the real line. A direct algorithm produces a general clas...
In this article, we develop a compact finite difference scheme for a variable-order-time fractional-sub-diffusion equation of a fourth-order derivative term via order reduction. The proposed scheme exhibits fourth-order convergence in space and secon...
Using the nonclassical symmetry of nonlinear reaction–diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen–Cahn–Hilliard equation. This models a phase field that gives a phenomenological...
Fractional differential equations describe nature adequately because of the symmetry properties which describe physical and biological processes. In this article, a fourth-order new implicit difference scheme is formulated and applied to solve the tw...
In this paper, a linearized mixed finite volume element (MFVE) scheme is proposed to solve the nonlinear time fractional fourth-order reaction–diffusion models with the Riemann–Liouville time fractional derivative. By introducing an auxil...
In this article, a new mixed finite element (MFE) algorithm is presented and developed to find the numerical solution of a two-dimensional nonlinear fourth-order Riemann–Liouville fractional diffusion-wave equation. By introducing two auxiliary...
This paper considers the numerical approximation to the fourth-order fractional diffusion-wave equation. Using a separation of variables, we can construct the exact solution for such a problem and then analyze its regularity. The obtained regularity...
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The fuzzy fractional differential equation explains more complex real-world phenomena than the fractional differential equation does. Therefore, numerous techniques have been timely derived to solve various fractional time-dependent models. In this p...
The entropy evolution behaviour of a partial differential equation (PDE) in conservation form, may be readily discerned from the sign of the local source term of Shannon information density. This can be easily used as a diagnostic tool to predict smo...
This paper presents a Crank–Nicolson mixed finite element method along with its reduced-order extrapolation model for a fourth-order nonlinear diffusion equation with Caputo temporal fractional derivative. By introducing the auxiliary variable...
This paper addresses how to use high-order diffusion to restore the wavelet coefficients in the wavelet domain. To avoid image distortion, wavelets with symmetry are used for image decomposition to obtain the wavelet coefficients of each sub-band. Du...
In a previous paper, we solved the partial differential equation of Mullins’ problem in the case of the evaporation–condensation in electronic devices and gave an exact solution relative to the geometric profile of the grain boundary groo...
This paper develops a fourth order entropy stable scheme to approximate the entropy solution of one-dimensional hyperbolic conservation laws. The scheme is constructed by employing a high order entropy conservative flux of order four in conjunction w...
A high-order compact (HOC) implicit difference scheme is proposed for solving three-dimensional (3D) unsteady reaction diffusion equations. To discretize the spatial second-order derivatives, the fourth-order compact difference operators are used, an...
Implicit integration factor (IIF) methods were developed for solving time-dependent stiff partial differential equations (PDEs) in literature. In [Jiang and Zhang, Journal of Computational Physics, 253 (2013) 368–388], IIF methods are designed to eff...
This study presents an efficient high-order radius function Hermite finite difference (RBF-HFD) scheme for the numerical solution of Caputo time-fractional sub-diffusion equations with integral boundary conditions. The spatial derivatives are approxi...
Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the no...
An implicit flux-corrected transport (FCT) and diffusion algorithm was developed and used in many gas discharge calculations. Such calculations require the use of a fine mesh where the electric field changes rapidly; that is, near electrodes or in a...
Numerical solutions of turbulent mass-transfer diffusion present challenges due to the nonlinearity of the elliptic–parabolic degeneracy of the mathematical models. Our main result in this paper concerns the development and implementation of an...
Singularly perturbed integro-partial differential equations with reaction–diffusion behavior present significant challenges due to boundary layers arising from small perturbation parameters, which complicate the development of accu...
Up to tenth-order finite difference schemes are proposed in this paper to solve one-dimensional advection-diffusion equation. The schemes based on high-order differences are presented using Taylor series expansion. To obtain the solutions, up to tent...
This paper presents a proposal of a time domain room acoustic solver using novel fourth-order accurate explicit time domain finite element method (TD-FEM), with demonstration of its applicability for practical room acoustic problems. Although time do...
Distributed-order, space-fractional diffusion equations are used to describe physical processes that lack power-law scaling. A fourth-order-accurate, A-stable time-stepping method was developed, analyzed, and implemented to solve inhomogeneous parabo...
In this paper, a type of high-order compact (HOC) finite difference method is developed for solving two- and three-dimensional unsteady convection diffusion reaction (CDR) equations with variable coefficients. Firstly, an HOC difference scheme is der...
A high-accuracy numerical method based on a sixth-order combined compact difference scheme and the method of lines approach is proposed for the advection–diffusion transport equation with variable parameters. In this approach, the partial differentia...
The decomposition of the Mueller matrix of blood films has been carried out using differential matrices with polarized and depolarized parts. The use of a coherent reference wave is applied and the algorithm of digital holographic reconstruction of t...
The efficiency of various numerical methods for solving Huxley’s equation—which includes a diffusion term and a nonlinear reaction term—is investigated. Conventional explicit finite difference algorithms often suffer from severe sta...
This paper constituted an extension of two previous studies concerning the mathematical development of the grain boundary grooving in polycrystalline thin films in the cases of evaporation/condensation and diffusion taken separately. The thermal groo...
The hydraulic design method of controllable blade angle for rotodynamic multiphase pump with impeller and diffuser is proposed. The distribution of blade angle along the meridional streamline is governed by the normalized fourth-order and first-order...
In the presented analysis, a heterogeneous diffusion is introduced to a magnetohydrodynamics (MHD) Darcy–Forchheimer flow, leading to an extended Darcy–Forchheimer model. The introduction of a generalized diffusion was proposed by Cohen a...
We derive a reaction–diffusion model with time-delayed nonlocal effects to study an epidemic’s spatial spread numerically. The model describes infected individuals in the latent period using a structured model with diffusion. The epidemic...
This paper presents a framework for inverse modeling of microwave filters based on a conditional diffusion model developed to address the intrinsic non-uniqueness of reconstructing coupling matrices from specified S-parameter responses. In the forwar...
By the iteration of the theta-formula and treating the neighbors explicitly such as the unconditionally positive finite difference (UPFD) methods, we construct a new 2-stage explicit algorithm to solve partial differential equations containing a diff...
The main objective of this work is to apply a novel and accurate algorithm for solving the second-order and fourth-order fractional diffusion-wave equations (FDWEs). First, the desired equation is reduced to the corresponding Volterra integral equati...
In recent years, the numerical theory of fractional models has received more and more attention from researchers, due to the broad and important applications in materials and mechanics, anomalous diffusion processes and other physical phenomena. In t...
In order to improve the performance of subsonic unmanned aerial vehicle (UAV), a knapsack S-duct intake has been designed. The influences of an S-bend diffuser on aerodynamic performance and electromagnetic performance were analyzed firstly. The visc...
High-performance liquid chromatography (HPLC) is a dynamic separation process with a lot of parameters having different roles. The equilibrium-dispersive model is relevant for simulating HPLC because it is relatively simple and suitable for high-effi...
This paper investigates a high-order numerical method based on a spatial compact exponential scheme for solving the time-fractional Black–Scholes model. Firstly, the original time-fractional Black–Scholes model is converted into an equiva...
An efficient adsorbent, CNTs–PAMAM–Ag, was prepared by grafting fourth-generation aromatic poly(amidoamine) (PAMAM) to carbon nanotubes (CNTs) and successive deposition of Ag nanoparticles. The FT–IR, XRD, TEM and XPS results confir...
Preventing or treating infections at implantation sites where the risk of bacterial contamination is high requires the development of intelligent drug delivery systems. The objective of this work was to develop a production method and characterizatio...
The focus of this study is on the impact of solar radiation reflected from the building façade to a pedestrian. The possibility of using high-reflectance technology on building façades was evaluated by using a two-dimensional simple building façade m...
The time-fractional Cattaneo equation is an equation where the fractional order
17 December 2019
In order to evaluate the environmental risk caused by land application of sewage sludge, leaching characteristics of heavy metals and plant nutrients in the sewage sludge immobilized by composite phosphorus-bearing materials were investigated. Their...
This article presents a modified version of the SVIR compartmental model for predicting the evolution of the COVID-19 pandemic, which incorporates vaccination and a saturated incidence rate, as well as piece-wise time-dependent parameters that enable...
The main contribution of this article is to propose a compact explicit scheme for solving time-dependent partial differential equations (PDEs). The proposed explicit scheme has an advantage over the corresponding implicit compact scheme to find solut...
Background: This study aimed to explore the differences in quantitative diffusion-weighted (DW) MRI parameters in oropharyngeal squamous cell carcinoma (OPC) based on Human Papillomavirus (HPV) status before and during radiotherapy (RT). Methods: Ech...
Orbital angular momentum (OAM) of optical vortex beams has been regarded as an independent physical dimension of light with predominant information-carrying potential. However, the presence of scattering environment and turbulent atmosphere scrambles...
A (2 + 1)-dimensional fourth order Burgers–KdV equation with variable coefficients (vcBKdV) is studied here and interesting wave-type solutions with variable amplitudes and velocities are reported. The model has been not previously studied in t...
This paper discusses the Darcy–Forchheimer three dimensional (3D) flow of a permeable nanofluid through a convectively heated porous extending surface under the influences of the magnetic field and nonlinear radiation. The higher-order chemical react...
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