scholarly journals Approximation for inextensible flows of curves in E³

2014 ◽  
Vol 32 (2) ◽  
pp. 45
Author(s):  
Talat Körpınar ◽  
Essin Turhan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
New Method ◽  
Frenet Frame ◽  
Partial Differential ◽  
Inextensible Flows ◽  
The Given

In this paper, we construct a new method for inextensible flows of curves in E³. Using the Frenet frame of the given curve, we present partial differential equations. We give some characterizations for curvatures of a curve in E³.

scholarly journals A New Method for Inextensible Flows of Timelike Curves in Minkowski Space-Time E14

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Talat Körpinar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Minkowski Space ◽  
Space Time ◽  
New Method ◽  
Frenet Frame ◽  
Partial Differential ◽  
Minkowski Space Time ◽  
Inextensible Flows ◽  
The Given

We construct a new method for inextensible flows of timelike curves in Minkowski space-time E14. Using the Frenet frame of the given curve, we present partial differential equations. We give some characterizations for curvatures of a timelike curve in Minkowski space-time E14.

scholarly journals On some nonlinear fractional PDEs in physics

BIBECHANA ◽  
2014 ◽  
Vol 12 ◽  
pp. 59-69
Author(s):  
Jamshad Ahmad ◽  
Syed Tauseef Mohyud-Din
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Variational Iteration Method ◽  
Mathematical Physics ◽  
Inverse Transformation ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Fractional Pdes ◽  
The Given ◽  
Nonlinear Nature

In this paper, we applied relatively new fractional complex transform (FCT) to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and Variational Iteration Method (VIM) is to find approximate solution of time- fractional Fornberg-Whitham and time-fractional Wu-Zhang equations. The results so obtained are re-stated by making use of inverse transformation which yields it in terms of original variables. It is observed that the proposed algorithm is highly efficient and appropriate for fractional PDEs arising in mathematical physics and hence can be extended to other problems of diversified nonlinear nature. Numerical results coupled with graphical representations explicitly reveal the complete reliability and efficiency of the proposed algorithm.  DOI: http://dx.doi.org/10.3126/bibechana.v12i0.11687BIBECHANA 12 (2015) 59-69 

scholarly journals Using Homo-Separation of Variables for Solving Systems of Nonlinear Fractional Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Abdolamir Karbalaie ◽  
Hamed Hamid Muhammed ◽  
Bjorn-Erik Erlandsson
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Separation Of Variables ◽  
General Purpose ◽  
New Method ◽  
Fractional Partial Differential Equations ◽  
Mathematical Methods ◽  
Partial Differential ◽  
Separation Of Variables Method ◽  
Linear And Nonlinear

A new method proposed and coined by the authors as the homo-separation of variables method is utilized to solve systems of linear and nonlinear fractional partial differential equations (FPDEs). The new method is a combination of two well-established mathematical methods, namely, the homotopy perturbation method (HPM) and the separation of variables method. When compared to existing analytical and numerical methods, the method resulting from our approach shows that it is capable of simplifying the target problem at hand and reducing the computational load that is required to solve it, considerably. The efficiency and usefulness of this new general-purpose method is verified by several examples, where different systems of linear and nonlinear FPDEs are solved.

New inextensible flows of principal normal spherical image

2017 ◽  
Vol 11 (01) ◽  
pp. 1850001 ◽  
Author(s):  
Talat Körpinar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Spherical Image ◽  
Partial Differential ◽  
Geometric Properties ◽  
Inextensible Flows

In this work, we study normal spherical indicatrices (images) in terms of inextensible flows in [Formula: see text]. We discuss the geometric properties of the normal spherical indicatrices. Furthermore, we give some new characterizations of curvatures in terms of some partial differential equations in [Formula: see text].

scholarly journals Exact, approximate solutions and error bounds for coupled implicit systems of partial differential equations

1992 ◽  
Vol 15 (4) ◽  
pp. 663-672
Author(s):  
Lucas Jódar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Initial Boundary ◽  
Approximate Solutions ◽  
Value Systems ◽  
Finite Domain ◽  
Partial Differential ◽  
Implicit Systems ◽  
Initial Boundary Value ◽  
The Given

In this paper coupled implicit initial-boundary value systems of second order partial differential equations are considered. Given a finite domain and an admissible errorϵan analytic approximate solution whose error is upper bounded byϵin the given domain is constructed in terms of the data.

scholarly journals VII. On the theory of the solution of a system of simultaneous non-linear partial ddifferential equations of the first order

1875 ◽  
Vol 23 (156-163) ◽  
pp. 510-510
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Arbitrary Constant ◽  
Partial Differential ◽  
First Order ◽  
Independent Variables ◽  
Linear Partial Differential Equations ◽  
Non Linear ◽  
The Given

Given an equation of the form z = ϕ ( x 1 , x 2 , ..... x n+m , a 1 , a 2 ,. . . . a n ), we obtain by differentiation with respect to each of the n + m independent variables x 1 , x 2 , ..... x n+m , and elimination of the n arbitrary constant a 1 , a 2 ,. . . . a n a system of m +1 non-linear partial differential equations of the first order. Of this system the given equation may be said to be "complete primitive.”

A hybrid analytical–numerical method for solving evolution partial differential equations. I. The half-line

2008 ◽  
Vol 464 (2095) ◽  
pp. 1823-1849 ◽  
Author(s):  
N Flyer ◽  
A.S Fokas
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Complex Plane ◽  
Complex Analysis ◽  
Variable Coefficients ◽  
Integral Representations ◽  
New Method ◽  
Half Line ◽  
Time Step ◽  
Partial Differential

A new method, combining complex analysis with numerics, is introduced for solving a large class of linear partial differential equations (PDEs). This includes any linear constant coefficient PDE, as well as a limited class of PDEs with variable coefficients (such as the Laplace and the Helmholtz equations in cylindrical coordinates). The method yields novel integral representations, even for the solution of classical problems that would normally be solved via the Fourier or Laplace transforms. Examples include the heat equation and the first and second versions of the Stokes equation for arbitrary initial and boundary data on the half-line. The new method has advantages in comparison with classical methods, such as avoiding the solution of ordinary differential equations that result from the classical transforms, as well as constructing integral solutions in the complex plane which converge exponentially fast and which are uniformly convergent at the boundaries. As a result, these solutions are well suited for numerics, allowing the solution to be computed at any point in space and time without the need to time step. Simple deformation of the contours of integration followed by mapping the contours from the complex plane to the real line allow for fast and efficient numerical evaluation of the integrals.

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