Local Linear Dependence of Linear Partial Differential Operators

Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

Linear Operators in the Theory of Partial Differential Equations

Quantifier Elimination for Approximate Factorization of Linear Partial Differential Operators

This paper looks at the feasibility of applying the quantifier elimination program QEPCAD-B to obtain quantifier-free conditions for the approximate factorization of a simple hyperbolic linear partial differential operator (LPDO) of order 2 over some given bounded rectangular domain in the plane. A condition for approximate factorization of such an operator to within some given tolerance over s...

Some Linear Operators in the Theory of Partial Differential Equations.

Image Zooming using Non-linear Partial Differential Equation

The main issue in any image zooming techniques is to preserve the structure of the zoomed image. The zoomed image may suffer from the discontinuities in the soft regions and edges; it may contain artifacts, such as image blurring and blocky, and staircase effects. This paper presents a novel image zooming technique using Partial Differential Equations (PDEs). It combines a non-linear Fourth-ord...