3,559 Results Found

This study focuses on the solution of the rotationally symmetric Rossler attractor by using the adaptive predictor–corrector algorithm (Apc-ABM-method) and the fractional Laplace decomposition method (ρ-Laplace DM). Furthermore, a compariso...

In this paper presents a new model procedure for the solution of the incompressible Navier-Stokes equations in primitive variables, using grid generation techniques. The time dependent momentum equations are solved explicitly for the velocity field u...

This article presents the applications of continuous symmetry groups to the computational fluid dynamics simulation of gas flow in porous media. The family of equations for one-phase flow in porous media, such as equations of gas flow with the Klinke...

This paper is devoted to shedding some light on the advantages of using tight frame systems for solving some types of fractional Volterra integral equations (FVIEs) involved by the Caputo fractional order derivative. A tight frame or simply framelet,...

In this article, a high-order time-stepping scheme based on the cubic interpolation formula is considered to approximate the generalized Caputo fractional derivative (GCFD). Convergence order for this scheme is (4−α), where α(0<&...

One-dimensional heat-conduction models in a semi-infinite domain, although forced convection obeys Newton’s law of cooling, are challenging to solve using standard integral transformation methods when the boundary condition φ(t) is an expon...

The mathematical structure of some natural phenomena of nonlinear physical and engineering systems can be described by a combination of fuzzy differential equations that often behave in a way that cannot be fully understood. In this work, an accurate...

This survey provides a comprehensive overview of the solutions to the matrix equation AXB=C over real numbers, complex numbers, quaternions, dual quaternions, dual split quaternions, and dual generalized commutative quaternions, including various spe...

In this work, we analyze a spherically symmetric 3D flow of a micropolar, viscous, polytropic, and heat-conducting real gas. In particular, we take as a domain the subset of R3 bounded by two concentric spheres that present solid thermoinsulated wall...

This article examines magnetohydrodynamic 3D nanofluid flow due to a rotating disk subject to Arrhenius activation energy and heat generation/absorption. Flow is created due to a rotating disk. Velocity, temperature and concentration slips at the sur...

We have investigated a two-dimensional radiative flow of a boundary layer nature. The fluid under consideration is carbon nanotube (CNT)-based nanofluid and it flows over a curved surface. The heat transfer through the flow is analyzed under the infl...

In the present paper, an algorithm for the numerical solution of the external Dirichlet generalized harmonic problem for a sphere by the method of probabilistic solution (MPS) is given, where “generalized” indicates that a boundary functi...

In this article, the numerical adaptive predictor corrector (Apc-ABM) method is presented to solve generalized Caputo fractional initial value problems. The Apc-ABM method was utilized to establish approximate series solutions. The presented techniqu...

The present study aimed at solving the stochastic generalized fractional diffusion equation (SGFDE) by means of the random finite difference method (FDM). Moreover, the conditions of mean square convergence of the numerical solution are studied and n...

The aim of this paper is to define the generalized discrete proportional derivative (GDPD) and illustrate the application of the Leibniz theorem, the binomial expansion, and Montmort’s formulas in the context of the generalized discrete proport...

A Lotka–Volterra-type system with porous diffusion, which can be used as an alternative model to the classical Lotka–Volterra system, is under study. Multiparameter families of exact solutions of the system in question are constructed and...

In this research study, we establish some necessary conditions to check the uniqueness-existence of solutions for a general multi-term ψ-fractional differential equation via generalized ψ-integral boundary conditions with respect to the generalized a...

In this paper, the goal is to revolve around discussing the stability of the Method of Fundamental Solutions (MFS) for the use case of wave-current interactions. Further, the reliability of Generating-Absorbing Boundary Conditions (GABCs) applied to...

The contribution of this paper is the proposal of a new receding horizon trajectory generation method for stratospheric airships’ return phase. Since the energy consumption, wind field and path constraints are restrictions during the return pha...

The inverse kinematics of robot manipulators is a crucial problem with respect to automatically controlling robots. In this work, a Newton-improved cyclic coordinate descent (NICCD) method is proposed, which is suitable for robots with revolute or pr...

This article describes the features of bio-convection and motile microorganisms in magnetized Burgers’ nanoliquid flows by stretchable sheet. Theory of Cattaneo–Christov mass and heat diffusions is also discussed. The Buongiorno phenomeno...

The entropy generation due to steady laminar forced convection fluid flow through parallel plates microchannel is investigated numerically. The effect of Knudsen, Reynolds, Prandtl, Eckert numbers and the nondimensional temperature difference on entr...

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...

In this paper, we present a novel algorithm for the computation of lightly robust optimal solutions for multi-objective optimization problems. To this end, we adapt the generalized cell mapping, originally designed for the global analysis of dynamica...

A B-spline function is a series of flexible elements that are managed by a set of control points to produce smooth curves. By using a variety of points, these functions make it possible to build and maintain complicated shapes. Any spline function of...

In this article, we present the extended simple equations method (SEsM) for finding exact solutions to systems of fractional nonlinear partial differential equations (FNPDEs). The expansions made to the original SEsM algorithm are implemented in seve...

This study examines the equilibrium structure and stability of white dwarfs, incorporating both isotropic and anisotropic pressure distributions. The Tolman–Oppenheimer–Volkoff (TOV) equation is numerically solved using the Chandrasekhar...

The example of two families of finite-difference schemes shows that, in general, the numerical solution of the Riemann problem for the generalized Hopf equation depends on the finite-difference scheme. The numerical solution may differ both quantitat...

The generalized eigenvalue problem for a symmetric definite matrix pencil obtained from finite-element modeling of electroelastic materials is solved numerically by the Lanczos algorithm. The mass matrix is singular in the considered problem, and the...

In this paper, we present a new computational method for solving linear Fredholm integral equations of the second kind, which is based on the use of B-spline quasi-affine tight framelet systems generated by the unitary and oblique extension principle...

Many security-related scenarios including cryptography depend on the random generation of passwords, permutations, Latin squares, CAPTCHAs and other types of non-numerical entities. Random generation of each entity type is a different problem with di...

High-quality, accurate grid generation is a critical challenge in the computational simulation of fluid flows around complex geometries. In particular, the accuracy of the grids is an effective factor in order to achieve a successful numerical simula...

Two different strategies are provided to generate solutions to the three-dimensional heat diffusion equation. The first strategy is inspired by the well-known one-dimensional heat polynomial, which consists of an infinite set of polynomials, which ar...

The article presents results of an analytical and numerical modeling of electron fluid motion and heat generation in a rectangular conductor at an alternating electric potential. The analytical solution is based on the series expansion solution (Four...

In this paper, two forms of an exact solution and an analytical–numerical solution of the three-term fractional differential equation with the Caputo derivatives are presented. The Prabhakar function and an asymptotic expansion are utilized to...

The present paper provides an accurate solution for finite plane strain bending under tension of a rigid/plastic sheet using a general material model of a strain-hardening viscoplastic material. In particular, no restriction is imposed on the depende...

In this work we generate the numerical solutions of Burgers’ equation by applying the Crank-Nicholson method and different schemes for solving nonlinear systems, instead of using Hopf-Cole transformation to reduce Burgers’ equation into the linear he...

In this work we present three new models of the fractal-fractional Ebola virus. We investigate the numerical solutions of the fractal-fractional Ebola virus in the sense of three different kernels based on the power law, the exponential decay and the...

This work concerns the numerical generation of stable solitary waves by using a piston-type wave maker and the propagation characteristics of a solitary wave in a step-type flume. The numerical generation of solitary waves was performed by solving N-...

We review and present several challenging model classes arising in the context of finding optimized object packings (OP). Except for the smallest and/or simplest general OP model instances, it is not possible to find their exact (closed-form) solutio...

This work introduces a general strategy to develop well-balanced high-order Discontinuous Galerkin (DG) numerical schemes for systems of balance laws. The essence of our approach is a local projection step that guarantees the exactly well-balanced ch...

The indentation of a power-law graded elastic half-space by a rigid counter body is considered in the framework of linear elasticity. Poisson’s ratio is assumed to be constant over the half-space. For indenters with an ellipsoidal power-law sha...

This study applies the space–time generalized finite difference scheme to solve nonlinear dispersive shallow water waves described by the modified Camassa–Holm equation, the modified Degasperis–Procesi equation, the Fornberg–W...

A two-dimensional heat diffusion problem with a heat source that is a quasilinear parabolic problem is examined analytically and numerically. Periodic boundary conditions are employed. As the problem is nonlinear, Picard’s successive approximat...

In this paper, we are interested in the numerical aspects of the class of generalized Riccati difference equations which are involved in linear quadratic (LQ) stochastic difference games. More specifically, we address the problem of the numerical com...

The existence of breather-type solutions, i.e., solutions that are periodic in time and exponentially localized in space, is a very unusual feature for continuum, nonlinear wave-type equations. Following an earlier work establishing a theorem for the...

In this paper, a new numerical technique is introduced to find the solution of the system of Volterra integral equations based on symmetric Bernstein polynomials. The use of Bernstein polynomials to find the numerical solutions of differential and in...

In this article, we consider approximate solutions by quadratic splines for a fractional differential equation with two Caputo fractional derivatives, the orders of which satisfy 1<α<2 and 0<β<1. Numerical computing schemes of...

Most engineering problems are described using differential equations, yet only a few can be solved analytically. Nonlinear differential equations are generally difficult to solve. The goal of numerical analysis is to minimize the difference between t...

The generalized Zakharov equation is a widely used and crucial model in plasma physics, which helps to understand wave particle interactions and nonlinear wave propagation in plasma. The solitary wave solution of this equation provides insights into...