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Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods
Issue:
Volume 6, Issue 6, December 2017
Pages:
238-242
Received:
8 August 2017
Accepted:
26 September 2017
Published:
7 November 2017
Abstract: In this paper, suggest anew two step iterative method for solving a nonlinear equation, which is derivative free by approximating a derivative in the iterative method by central difference with one parameter θ. The anew derivative free iterative method has a convergence of order four and computational cost the family requires three evaluations of functions per iteration. Numerical experiments show that the proposed a method is comparable to the existing method in terms of the number of iterations.
Abstract: In this paper, suggest anew two step iterative method for solving a nonlinear equation, which is derivative free by approximating a derivative in the iterative method by central difference with one parameter θ. The anew derivative free iterative method has a convergence of order four and computational cost the family requires three evaluations of f...
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A Comparative Study on Fourth Order and Butcher’s Fifth Order Runge-Kutta Methods with Third Order Initial Value Problem (IVP)
Md. Babul Hossain,
Md. Jahangir Hossain,
Md. Musa Miah,
Md. Shah Alam
Issue:
Volume 6, Issue 6, December 2017
Pages:
243-253
Received:
26 September 2017
Accepted:
8 October 2017
Published:
8 November 2017
Abstract: In this paper, Butcher’s fifth order Runge-Kutta (RK5) and fourth order Runge-Kutta (RK4) methods have been employed to solve the Initial Value Problems (IVP) involving third order Ordinary Differential Equations (ODE). These two proposed methods are quite proficient and practically well suited for solving engineering problems based on such problems. To obtain the accuracy of the numerical outcome for this study, we have compared the approximate results with the exact results and found a good agreement between the exact and approximate solutions. In addition, to achieve more accuracy in the solution, the step size needs to be very small. Moreover, the error terms have been analyzed for these two methods and also compared by an appropriate example.
Abstract: In this paper, Butcher’s fifth order Runge-Kutta (RK5) and fourth order Runge-Kutta (RK4) methods have been employed to solve the Initial Value Problems (IVP) involving third order Ordinary Differential Equations (ODE). These two proposed methods are quite proficient and practically well suited for solving engineering problems based on such problem...
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Some Identities Related with the Higher-order Deformed Degenerate Bernoulli and Euler Polynomials
Issue:
Volume 6, Issue 6, December 2017
Pages:
254-258
Received:
25 July 2017
Accepted:
10 November 2017
Published:
15 December 2017
Abstract: Recently, Kim-Kim (2016-2017) studied simmetric identities of higher-order degenerate Bernoulli and Euler polynomials which were defined by Carlitz (1979). In this paper, we define the higher-order deformed degenerate Bernoulli and Euler polynomials which are modified the higher-order degenerate Bernoulli and Euler polynomials. We also investigate some interesting identities for the the higher-order deformed degenerate Bernoulli and Euler polynomials.
Abstract: Recently, Kim-Kim (2016-2017) studied simmetric identities of higher-order degenerate Bernoulli and Euler polynomials which were defined by Carlitz (1979). In this paper, we define the higher-order deformed degenerate Bernoulli and Euler polynomials which are modified the higher-order degenerate Bernoulli and Euler polynomials. We also investigate ...
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Schultz and Modified Schultz Polynomials of Cog-Complete Bipartite Graphs
Ahmed Mohammed Ali,
Haitham Nashwan Mohammed
Issue:
Volume 6, Issue 6, December 2017
Pages:
259-264
Received:
9 September 2017
Accepted:
9 November 2017
Published:
18 December 2017
Abstract: Let G be a simple connected graph, the vertex- set and edge- set of G are denoted by V(G) and E(G), respectively. The molecular graph G, the vertices represent atoms and the edges represent bonds. In graph theory, we have many invariant polynomials and many invariant indices of a connected graph G. Topological indices based on the distance between the vertices of a connected graph are widely used in theoretical chemistry to establish relation between the structure and the properties of molecules. The coefficients of polynomials are also important in the knowledge some properties in application chemistry. The Schultz and modified Schultz polynomials, Schultz and modified Schultz indices and average distance of Schultz and modified Schultz of Cog-complete bipartite graphs are obtained in this paper.
Abstract: Let G be a simple connected graph, the vertex- set and edge- set of G are denoted by V(G) and E(G), respectively. The molecular graph G, the vertices represent atoms and the edges represent bonds. In graph theory, we have many invariant polynomials and many invariant indices of a connected graph G. Topological indices based on the distance between ...
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MHD Boundary Layer Flow of Nanofluid over a Continuously Moving Stretching Surface
Haroon Rasheed,
Abdul Rehman,
Naveed Sheikh,
Saleem Iqbal
Issue:
Volume 6, Issue 6, December 2017
Pages:
265-270
Received:
25 October 2017
Accepted:
13 November 2017
Published:
25 December 2017
Abstract: The present investigation provides an insight in the steady, incompressible and electrically conducting boundary layer flow of viscoelastic nanofluid flowing due to a moving, linearly stretched surface. The governing system of nonlinear partial differential equations is simplified by considering Boussinesq and boundary layer approximations. An analytical solution of the resulting nonlinear ordinary differential equations for momentum, energy and concentration profiles is obtained using the homotopy analysis method (HAM).
Abstract: The present investigation provides an insight in the steady, incompressible and electrically conducting boundary layer flow of viscoelastic nanofluid flowing due to a moving, linearly stretched surface. The governing system of nonlinear partial differential equations is simplified by considering Boussinesq and boundary layer approximations. An anal...
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