Transforms from differential equations to difference equations and vice-versa applied to computer control systems

Partial Differential Equations applied to Medical Image ‎Segmentation

‎This paper presents an application of partial differential equations(PDEs) for the segmentation of abdominal and thoracic aortic in CTA datasets. An important challenge in reliably detecting aortic is the need to overcome problems associated with intensity inhomogeneities. Level sets are part of an important class of methods that utilize partial differential equations (PDEs) and have been exte...

Difference Equations and Z - Transforms

Gröbner Bases Applied to Systems of Linear Difference Equations

In this paper we consider systems of partial (multidimensional) linear difference equations. Specifically, such systems arise in scientific computing under discretization of linear partial differential equations and in computational high energy physics as recurrence relations for multiloop Feynman integrals. The most universal algorithmic tool for investigation of linear difference systems is b...

Groebner Bases Applied to Systems of Linear Difference Equations

In this paper we consider systems of partial (multidimensional) linear difference equations. Specifically, such systems arise in scientific computing under discretization of linear partial differential equations and in computational high energy physics as recurrence relations for multiloop Feynman integrals. The most universal algorithmic tool for investigation of linear difference systems is b...

Nonstandard finite difference schemes for differential equations

In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...