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In this research, we present a hybrid method which combination of simplified reproducing kernel method (SRKM) and asymptotic expansion for solving singularly perturbed convection–diffusion problems. According to the hybrid method, firstly asymptotic expansion formed on boundary layer domain and then terminal value problem solved via SRKM on regular domain. To apply the SRKM, some special Hilbert spaces...
In this work a new integral transform is introduced and applied to solve higher order linear ordinary Laguerre and Hermite differential equations. We compare present transform with other method such as Frobenius Method.
A systematic description of actions of the divided differences operators on power and exponential functions is given. The results of actions of these operators on entire functions are presented by the matrices whose elements are functions of coefficients of a characteristic (pivot) polynomial. Effective algorithms of calculation of the matrices are constructed using the properties of the companion...
In this paper, the authors investigate the numerical solutions of two-dimensional reaction–diffusion equations with Neumann boundary conditions, known as Brusselator model, using Chebyshev pseudospectral method. The proposed methods are established in both time and space to approximate the solutions and prove the stability analysis of the equations. Higher order Chebyshev differential matrix is used...
A discrete-time batch service queue with batch renewal input and random serving capacity rule under the late arrival delayed access system, has recently appeared in the literature (Barbhuiya and Gupta in Queueing Syst 91(3):347–365, 2019b). In this paper, we consider the same model under the early arrival system, since it is more applicable in telecommunication systems where an arriving batch of packets...
Here, $$\tan \left( \frac{\phi (\xi )}{2}\right) $$ tanϕ(ξ)2 -expansion method is being applied on $$(1+2)$$ (1+2) -dimensional nonlinear Schrödinger equation (NLSE) with dual power law nonlinearity. Spatial solitons and optial nonlinearities in materials like photovoltaic–photorefractive, polymer and organic can be identified by seeking help from NLSE with dual power law nonlinearity. Abundant exact...
The present manuscript deals with the generation of flexural gravity waves due to transient axi-symmetric disturbances in two-layer fluid. Roles of structural rigidity and compressive force on the transient flexural gravity wave motion are analyzed under the assumption of small amplitude water wave theory and structural responses in the case of finite water depth. Using Laplace and Hankel transforms,...
This article deals with a singularly perturbed delay differential equation involving two small parameters. First, an upwind scheme is proposed on the fitted Shishkin mesh. The method is shown to be first order convergent. Then a hybrid scheme consisting of the midpoint upwind scheme in the outer region and the central difference scheme in the inner region is proposed. The error analysis is carried...
In this manuscript, we have proposed the scheme of dual combination combination multiswitching synchronization for fractional order hyperchaotic nonlinear dynamical systems. The proposed scheme has been applied to fractional order hyperchaotic systems. To verify the results, numerical simulations are carried out using Matlab by taking the hyperchaotic Lü system, Lorenz system, Chen system and the...
A numerical direct method for solving two-dimensional linear and nonlinear Fredholm integral equations of the first kind based on Haar wavelet is introduced. The main characteristic of the method is that, unlike several other methods, it does not involve numerical integration, which leads to higher accuracy and quick computations as well. Further more an estimation of error bound for the present method...
In this paper, we discuss the multi-layer perceptron artificial neural network technique for the solution of homogeneous and non-homogeneous Lane–Emden type differential equations. Our aim is to produce an optimal solution of Lane–Emden equations with less computation using multi-layer perceptron artificial neural network technique, comparatively other numerical techniques. Several test examples have...
Demand for several variety of commodity depends on its nature like; price, corrosion and time. In most inventory models demand is considered constant or time-dependent. In this study, we set up a deterministic EOQ for weakening stuffs when demand is quadratic time linked. Shortages are permitted and totally backlogged. Mathematical representation is derived and then some constructive outcomes is framed...
A multi-objective, multi item inventory model is constructed for deteriorating items where the demand is considered as exponential time function under limited storage space as well as budget. By using Fuzzy non linear programming (FNLP) and Intutionistic fuzz optimization (IFO) techniques results are obtained and then compared. The objective of this work is to use FNLP and IFO techniques for multi-objective...
We investigate the impact of nonlinear thermal radiation and variable transport properties on the two-dimensional flow of an electrically conducting Casson nanofluid containing gyrotactic microorganisms along a moving wedge. In some previous studies, it has been assumed that the fluid viscosity and thermal conductivity are temperature dependent. However, this study assumes that the fluid viscosity,...
Integral representations for the velocity vector, microrotation vector and the scalar microstretch function are derived for the class of microstretch fluids under the assumption of creeping and incompressible steady motion. In deriving these representations, we used previous known results solutions corresponding to a concentrated force, a concentrated couple and a concentrated microstretch force density...
A new numerical method is developed for approximating the solution of the fourth-order boundary-value problems with the help fractal quintic spline. The proposed method has second-order convergence. Numerical examples are experimented for the numerical illustration of the proposed method. It is shown that the method developed in this paper is more efficient than the method developed by the quintic...
Very recently Srivastava et al. (Russ J Math Phys 25(1):116–138, 2018) have introduced the incomplete H-functions and investigated their several interesting properties, for example, decomposition and reduction formulas, derivative formulas, and various integral transforms. They also pointed out potential applications of many of those incomplete special functions, which are specialized from the incomplete...
The numerical exploration of three dimensional Carreau magneto Nanofluid flow through a stretching sheet has been bestowed with considering nonlinear thermal radiation, velocity, thermal and mass slips. The heat and mass transfer attributes have been reported under the existing important variables in this work. The elementary equations which influence flow are remoulded to a system through the similarity...
In this work, the KdV equation with conformable derivative and dual-power law nonlinearity is considered. It is exceedingly used as a model to depict the feeble nonlinear long waves in different fields of sciences. Furthermore, it explains the comparable effects of weak dispersion and weak nonlinearity on the evolvement of the nonlinear waves. Using the Jacobi elliptic function expansion method, new...
The equivalent linearization method based on weighted averaging is employed to obtain a approximate solution for a generalized nonlinear oscillator given in the form of $$ \ddot{u} + \alpha u + \beta u^{m} + \frac{{\gamma u^{n} }}{{\mu + \delta u^{p} }} = 0. $$ u¨+αu+βum+γunμ+δup=0. The amplitude–frequency relationship of oscillation is given in a closed-form. Accuracy of the approximate solution...
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