17 papers · ranked by Valyu relevance
Sandip Moi, Suvankar Biswas, Smita Pal(Sarkar)
In this article, some properties of neutrosophic derivative and neutrosophic numbers have been presented. This properties have been used to develop the neutrosophic differential calculus. By considering different types of first- and second-order derivatives, different kind of systems of derivatives have been developed.…
Yuanheng Wang, Barrira Jurrat, Muddasir Ejaz, Muhammad Azeem + 2 more
'M. I. Elashiry' 'Rehana Naz'] In this paper, the existence and uniqueness of solution for a fractional differential model involving well-posed boundary conditions and implicit fractional differential equation is considered. The desired goals are achieved by using Banach contraction principle and Scheafer’s fixed point…
Mehmet Pakdemirli
The recently developed perturbation iteration method is applied to boundary layer type singular problems for the first time. As a preliminary work on the topic, the simplest algorithm of PIA(1,1) is employed in the calculations. Linear and nonlinear problems are solved to outline the basic ideas of the new solution…
P. K. Pandey
In this article, we present a novel second order numerical method for solving third order boundary value problems using the quartic polynomial splines. We establish the convergence of the method. We present numerical experiments to demonstrate the efficiency of the method and validity of our second order method, which…
Ahmed Salem Heilat, Nur Nadiah Abd Hamid, Ahmad Izani Md. Ismail
A method based on extended cubic B-spline is proposed to solve a linear system of second-order boundary value problems. In this method, two free parameters, $\lambda _{1}$ and $\lambda _{2}$, play an important role in producing accurate results. Optimization of these parameters are carried out and the truncation error…
Salima Kouser, Shafiq Ur Rehman, Yasser Elmasry, Waqar Azeem Khan + 3 more
'Fayyaz Ahmad' 'Hamza Khan' 'B. Omkar Lakshmi Jagan'] The Newton method is a classical method for solving systems of nonlinear equations and offers quadratic convergence. The order of convergence of the Newton method is optimal as it requires one evaluation for the system of nonlinear equations and the second for the…
Chengbo Zhai, Mengru Hao
By using Krasnoselskii's fixed point theorem, we study the existence of at least one or two positive solutions to a system of fractional boundary value problems given by −D0+ν1y1(t) = λ1a1(t)f(y1(t), y2(t)), − D0+ν2y2(t) = λ2a2(t)g(y1(t), y2(t)), where D0+ν is the standard Riemann-Liouville fractional derivative, ν1…
Suheel Abdullah Malik, Ijaz Mansoor Qureshi, Muhammad Amir, Ihsanul Haq
'Ihsanul Haq'] We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error…
Fellek Sabir Andisso, Gemechis File Duressa
The solutions of two parameters singularly perturbed boundary value problems typically exhibit two boundary layers. Because of the presence of these layers standard numerical methods fail to give accurate approximations. This paper introduces a numerical treatment of a class of two parameters singularly perturbed…
Evgenii S. Baranovskii, Hang Xu, Jifeng Cui
In this paper, we obtain new exact solutions for the unidirectional non-isothermal flow of a second grade fluid in a plane channel with impermeable solid walls, taking into account the fluid energy dissipation (mechanical-to-thermal energy conversion) in the heat transfer equation. It is assumed that the flow is…
Ahmed Alsaedi, Sotiris K. Ntouyas, Bashir Ahmad
By employing a nonlinear alternative for contractive maps, we investigate the existence of solutions for a boundary value problem of fractional q-difference inclusions with nonlocal substrip type boundary conditions. The main result is illustrated with the aid of an example.
Anthony N. Johnson, T.V. Hromadka II
The complex variable boundary element method (CVBEM) has been shown to be a mathematically sound approach for modeling two-dimensional potential problems . The foundations of the CVBEM method rests in complex variable theory, namely, the Cauchy integral formula. It tells us that if a function, ω, is analytic within and…
Huashui Zhan, Yongping Li
The degenerate parabolic equations from the reaction-diffusion problems are considered on an unbounded domain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…
Getu M. Wondimu, Mesfin M. Woldaregay, Gemechis F. Duressa, Tekle G. Dinka
'Tekle G. Dinka'] Objectives In this article, a singularly perturbed delay reaction-diffusion problem with nonlocal boundary conditions is considered. The exponential fitting factor is introduced to treat the solutions inside the boundary layer which occur due to perturbation parameter. The considered problem has…
Saima Bibi, Syeda Tehmina Ejaz
In numerical methods, fine mesh sizes are often necessary to obtain highly accurate solutions of the differential equations and this increases the memory consumption and decreases the efficiency of the calculation. This paper presents a subdivision collocation algorithm of time-fractional advection diffusion equation…
Yanjie Zhou, Zhendong Luo, Fei Teng
In this article, we first develop a semi-discretized Crank-Nicolson format about time for the two-dimensional non-stationary Stokes equations about vorticity-stream functions and analyze the existence, uniqueness, stability, and convergence of the semi-discretized Crank-Nicolson solutions. Then we establish a fully…
Zhimin Hong, Zaizai Yan, Jiao Yan, Guido Germano
In this paper, a randomized numerical approach is used to obtain approximate solutions for a class of nonlinear Fredholm integral equations of the second kind. The proposed approach contains two steps: at first, we define a discretized form of the integral equation by quadrature formula methods and solution of this…