A Numerical Computational Method for Image Zooming

2014 ◽  
Vol 543-547 ◽  
pp. 2300-2303
Author(s):  
Li Hua Sun ◽  
En Liang Zhao ◽  
Feng Ying Wang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Difference Scheme ◽  
Diffusion Model ◽  
Anisotropic Diffusion ◽  
Integral Method ◽  
Computational Method ◽  
Partial Differential ◽  
The Difference

In this paper, we make use of the integral method which is commonly used in partial differential equations to get the difference scheme on five points, and then construct an anisotropic diffusion model based on the partial differential equation. The numerical experimental results show the diffusion model can effectively magnify the image, and can keep the edge character and details of the image. It is proved that the numerical computational method proposed for solving the model is very effective.

scholarly journals A Stable Difference Scheme for a Third-Order Partial Differential Equation

2018 ◽  
Vol 64 (1) ◽  
pp. 1-19 ◽  
Author(s):  
A Ashyralyev ◽  
Kh Belakroum
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Approximate Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Scheme ◽  
Nonlocal Boundary ◽  
Order Partial Differential Equation ◽  
Third Order ◽  
Partial Differential

The nonlocal boundary-value problem for a third order partial differential equation in a Hilbert space H with a self-adjoint positive definite operator A is considered. A stable three-step difference scheme for the approximate solution of the problem is presented. The main theorem on stability of this difference scheme is established. In applications, the stability estimates for the solution of difference schemes of the approximate solution of three nonlocal boundary value problems for third order partial differential equations are obtained. Numerical results for oneand two-dimensional third order partial differential equations are provided.

Hybrid solution of partial differential equations by application of invariant imbedding to the serial method

SIMULATION ◽  
1971 ◽  
Vol 17 (4) ◽  
pp. 147-153 ◽  
Author(s):  
Paul Nelson ◽  
Donald W. Altom
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Time Discretization ◽  
Computational Method ◽  
Computational Results ◽  
Invariant Imbedding ◽  
Partial Differential ◽  
Hybrid Solution

This paper presents a hybrid computational method in which invariant imbedding is used to effect analog solution of the boundary-value problems which typically result from time discretization of a partial differential equation. The method is developed from fundamentals, scaling rules are derived, computational results are presented and discussed, and possible extensions are mentioned.

Adaptive Diversification and Speciation as Pattern Formation in Partial Differential Equation Models

2011 ◽  
Author(s):  
Michael Doebeli
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Pattern Formation ◽  
Differential Equations ◽  
Adaptive Dynamics ◽  
Partial Differential ◽  
Adaptive Diversification ◽  
Differential Equation Models ◽  
Phenotype Distribution

This chapter discusses partial differential equation models. Partial differential equations can describe the dynamics of phenotype distributions of polymorphic populations, and they allow for a mathematically concise formulation from which some analytical insights can be obtained. It has been argued that because partial differential equations can describe polymorphic populations, results from such models are fundamentally different from those obtained using adaptive dynamics. In partial differential equation models, diversification manifests itself as pattern formation in phenotype distribution. More precisely, diversification occurs when phenotype distributions become multimodal, with the different modes corresponding to phenotypic clusters, or to species in sexual models. Such pattern formation occurs in partial differential equation models for competitive as well as for predator–prey interactions.

XIII.—Partial Differential Equations and the Calculus of Variations

1927 ◽  
Vol 46 ◽  
pp. 126-135 ◽  
Author(s):  
E. T. Copson
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Calculus Of Variations ◽  
Order Equation ◽  
Second Order ◽  
Physical Problem ◽  
Partial Differential ◽  
Hamiltonian Principle

A partial differential equation of physics may be defined as a linear second-order equation which is derivable from a Hamiltonian Principle by means of the methods of the Calculus of Variations. This principle states that the actual course of events in a physical problem is such that it gives to a certain integral a stationary value.

scholarly journals Patch Similarity Modulus and Difference Curvature Based Fourth-Order Partial Differential Equation for Image Denoising

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Yunjiao Bai ◽  
Quan Zhang ◽  
Hong Shangguan ◽  
Zhiguo Gui ◽  
Yi Liu ◽  
...  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Image Denoising ◽  
Fourth Order ◽  
Objective Evaluation ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
The Difference ◽  
Adaptively Adjusting ◽  
Difference Curvature

The traditional fourth-order nonlinear diffusion denoising model suffers the isolated speckles and the loss of fine details in the processed image. For this reason, a new fourth-order partial differential equation based on the patch similarity modulus and the difference curvature is proposed for image denoising. First, based on the intensity similarity of neighbor pixels, this paper presents a new edge indicator called patch similarity modulus, which is strongly robust to noise. Furthermore, the difference curvature which can effectively distinguish between edges and noise is incorporated into the denoising algorithm to determine the diffusion process by adaptively adjusting the size of the diffusion coefficient. The experimental results show that the proposed algorithm can not only preserve edges and texture details, but also avoid isolated speckles and staircase effect while filtering out noise. And the proposed algorithm has a better performance for the images with abundant details. Additionally, the subjective visual quality and objective evaluation index of the denoised image obtained by the proposed algorithm are higher than the ones from the related methods.

III. On the differential equations of dynamics. A sequel to a paper on simultaneous differential equations

1863 ◽  
Vol 12 ◽  
pp. 420-424
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Dynamical Problem ◽  
General Character ◽  
Partial Differential ◽  
Central Function ◽  
First Order ◽  
Linear Partial Differential Equations

Jacobi in a posthumous memoir, which has only this year appeared, has developed two remarkable methods (agreeing in their general character, but differing in details) of solving non-linear partial differential equations of the first order, and has applied them in connexion with that theory of the differential equations of dynamics which was established by Sir W. R. Hamilton in the 'Philosophical Transactions’ for 1834-35. The knowledge, indeed, that the solution of the equation of a dynamical problem is involved in the discovery of a single central function, defined by a single partial differential equation of the first order, does not appear to have been hitherto (perhaps it will never be) very fruitful in practical results.

scholarly journals Comparison Theorem for Nonlinear Path-Dependent Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Falei Wang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Comparison Theorem ◽  
Parabolic Partial Differential Equation ◽  
Basic Variable ◽  
Partial Differential ◽  
Fully Nonlinear ◽  
Path Dependent

We introduce a type of fully nonlinear path-dependent (parabolic) partial differential equation (PDE) in which the pathωton an interval [0,t] becomes the basic variable in the place of classical variablest,x∈[0,T]×ℝd. Then we study the comparison theorem of fully nonlinear PPDE and give some of its applications.

scholarly journals Invariant measures for the flow of a first order partial differential equation

1985 ◽  
Vol 5 (3) ◽  
pp. 437-443 ◽  
Author(s):  
R. Rudnicki
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Invariant Measures ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
First Order

AbstractWe prove that the dynamical systems generated by first order partial differential equations are K-flows and chaotic in the sense of Auslander & Yorke.

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