Constructing Artistic Surface Modeling Design Based on Nonlinear Over-limit Interpolation Equation

Abstract The digital and physical methods of establishing minimal curved surfaces are the basis for realizing the design of the minimal curved surface modeling structure. Based on this research background, the paper showed an artistic surface modeling method based on nonlinear over-limit difference equations. The article combines parameter optimization and 3D modeling methods to model the constructed surface modeling. The research found that the nonlinear out-of-limit difference equation proposed in the paper is more accurate than the standard fractional differential equation algorithm. For this reason, the method can be extended and applied to the design of artistic surface modeling.

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p-adic confluence of q-difference equations

Compositio Mathematica ◽

10.1112/s0010437x07003454 ◽

2008 ◽

Vol 144 (4) ◽

pp. 867-919 ◽

Cited By ~ 6

Author(s):

Andrea Pulita

Keyword(s):

Differential Equation ◽

Difference Equation ◽

Differential Equations ◽

Difference Equations ◽

Root Of Unity

AbstractWe develop the theory of p-adic confluence of q-difference equations. The main result is the fact that, in the p-adic framework, a function is a (Taylor) solution of a differential equation if and only if it is a solution of a q-difference equation. This fact implies an equivalence, called confluence, between the category of differential equations and those of q-difference equations. We develop this theory by introducing a category of sheaves on the disk D−(1,1), for which the stalk at 1 is a differential equation, the stalk at q isa q-difference equation if q is not a root of unity, and the stalk at a root of unity ξ is a mixed object, formed by a differential equation and an action of σξ.

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Exact Solutions for Fractional Differential-Difference Equations by (G'/G)-Expansion Method with Modified Riemann-Liouville Derivative

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.2014.m798 ◽

2016 ◽

Vol 8 (2) ◽

pp. 293-305 ◽

Cited By ~ 10

Author(s):

Ahmet Bekir ◽

Ozkan Guner ◽

Burcu Ayhan ◽

Adem C. Cevikel

Keyword(s):

Difference Equation ◽

Exact Solutions ◽

Difference Equations ◽

Applied Mathematics ◽

Expansion Method ◽

New Exact Solutions ◽

Liouville Derivative ◽

Nonlinear Lattice ◽

Fractional Differential ◽

Differential Difference Equation

AbstractIn this paper, the (G'/G)-expansion method is suggested to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann-Liouville derivative. The fractional complex transform is proposed to convert a fractional partial differential difference equation into its differential difference equation of integer order. With the aid of symbolic computation, we choose nonlinear lattice equations to illustrate the validity and advantages of the algorithm. It is shown that the proposed algorithm is effective and can be used for many other nonlinear lattice equations in mathematical physics and applied mathematics.

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A class of big (p,q)-Appell polynomials and their associated difference equations

Filomat ◽

10.2298/fil1910085s ◽

2019 ◽

Vol 33 (10) ◽

pp. 3085-3121

Author(s):

H.M. Srivastava ◽

B.Y. Yaşar ◽

M.A. Özarslan

Keyword(s):

Differential Equation ◽

Difference Equation ◽

Recurrence Relation ◽

Difference Equations ◽

Recurrence Relations ◽

Bernoulli Polynomials ◽

Equivalence Theorem ◽

Euler Polynomials ◽

Appell Polynomials ◽

Special Case

In the present paper, we introduce and investigate the big (p,q)-Appell polynomials. We prove an equivalance theorem satisfied by the big (p, q)-Appell polynomials. As a special case of the big (p,q)- Appell polynomials, we present the corresponding equivalence theorem, recurrence relation and difference equation for the big q-Appell polynomials. We also present the equivalence theorem, recurrence relation and differential equation for the usual Appell polynomials. Moreover, for the big (p; q)-Bernoulli polynomials and the big (p; q)-Euler polynomials, we obtain recurrence relations and difference equations. In the special case when p = 1, we obtain recurrence relations and difference equations which are satisfied by the big q-Bernoulli polynomials and the big q-Euler polynomials. In the case when p = 1 and q ? 1-, the big (p,q)-Appell polynomials reduce to the usual Appell polynomials. Therefore, the recurrence relation and the difference equation obtained for the big (p; q)-Appell polynomials coincide with the recurrence relation and differential equation satisfied by the usual Appell polynomials. In the last section, we have chosen to also point out some obvious connections between the (p; q)-analysis and the classical q-analysis, which would show rather clearly that, in most cases, the transition from a known q-result to the corresponding (p,q)-result is fairly straightforward.

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The Solution of Difference Equations by Continued Fractions

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500029576 ◽

1915 ◽

Vol 34 ◽

pp. 61-75

Author(s):

J. A. Strang

Keyword(s):

Differential Equation ◽

Ordinary Differential Equation ◽

Difference Equation ◽

Difference Equations ◽

Continued Fractions ◽

Special Form ◽

Quadratic Equation ◽

Similar Process ◽

Image Position ◽

Bilinear Equation

The theorems which furnish in C.F. form the roots of a quadratic equation, and the similar process which leads to particular integrals of an ordinary differential equation of the second order, may be applied to certain types of difference equation. The types which suggest themselves for examination arethe bilinear equation, anda special form of the linear equation; the coefficients are functions of r, and s is constant.

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Best difference equation approximation to Duffing's equation

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000000308 ◽

1982 ◽

Vol 23 (4) ◽

pp. 349-356 ◽

Cited By ~ 22

Author(s):

Renfrey B. Potts

Keyword(s):

Differential Equation ◽

Difference Equation ◽

Difference Equations ◽

Duffing's Equation ◽

Duffing’S Equation

AbstractDuffing's differential equation in its simplest form can be approximated by a variety of difference equations. It is shown how to choose a ‘best’ difference equation in the sense that the solutions of this difference equation are successive discrete exact values of the solution of the differential equation.

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Meromorphic solutions of difference equations originated from Schwarzian differential equation

Filomat ◽

10.2298/fil2006003l ◽

2020 ◽

Vol 34 (6) ◽

pp. 2003-2015

Author(s):

Shuang-Ting Lan ◽

Zhi-Bo Huang ◽

Chuang-Xin Chen

Keyword(s):

Differential Equation ◽

Positive Integer ◽

Difference Equation ◽

Rational Function ◽

Finite Order ◽

Difference Equations ◽

Meromorphic Functions ◽

Meromorphic Solution ◽

Meromorphic Solutions ◽

The Difference

Let f (z) be a meromorphic functions with finite order , R(z) be a nonconstant rational function and k be a positive integer. In this paper, we consider the difference equation originated from Schwarzian differential equation, which is of form [?3f(z)?f(z)- 3/2(?2|(z))2]k = R(z)(?f (z))2k. We investigate the uniqueness of meromorphic solution f of difference Schwarzian equation if f shares three values with any meromrphic function. The exact forms of meromorphic solutions f of difference Schwarzian equation are also presented.

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