Formulas for Numerical Integration of First and Second Order Differential Equations in the Complex Plane

1950 ◽  
Vol 29 (1-4) ◽  
pp. 207-216 ◽  
Author(s):  
Herbert E. Salzer
Keyword(s):  
Differential Equations ◽  
Numerical Integration ◽  
Complex Plane ◽  
Second Order ◽  
Second Order Differential Equations

scholarly journals Hausdorff Dimension of Escaping Sets of Nevanlinna Functions

2019 ◽  
Author(s):  
Weiwei Cui
Keyword(s):  
Hausdorff Dimension ◽  
Differential Equations ◽  
Complex Plane ◽  
Meromorphic Functions ◽  
Second Order ◽  
Hausdorff Dimensions ◽  
Second Order Differential Equations ◽  
Schwarzian Derivatives ◽  
Nevanlinna Functions

Abstract We determine the exact values of Hausdorff dimensions of escaping sets of meromorphic functions with polynomial Schwarzian derivatives. This will follow from the relation between these functions and the second-order differential equations in the complex plane.

scholarly journals On Generalisation of Polynomials in Complex Plane

2010 ◽  
Vol 2010 ◽  
pp. 1-9
Author(s):  
Maslina Darus ◽  
Rabha W. Ibrahim
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Complex Plane ◽  
Special Functions ◽  
Laguerre Polynomials ◽  
Second Order ◽  
Second Order Differential Equations

The generalised Bell and Laguerre polynomials of fractional-order in complex z-plane are defined. Some properties are studied. Moreover, we proved that these polynomials are univalent solutions for second order differential equations. Also, the Laguerre-type of some special functions are introduced.

Banach Lie Algebroids

2011 ◽  
Vol 57 (2) ◽  
pp. 409-416
Author(s):  
Mihai Anastasiei
Keyword(s):  
Differential Equations ◽  
Smooth Manifold ◽  
Vector Bundles ◽  
Second Order ◽  
Lie Algebroids ◽  
Second Order Differential Equations

Banach Lie AlgebroidsFirst, we extend the notion of second order differential equations (SODE) on a smooth manifold to anchored Banach vector bundles. Then we define the Banach Lie algebroids as Lie algebroids structures modeled on anchored Banach vector bundles and prove that they form a category.

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