scholarly journals A Symbolic-Numeric Validation Algorithm for Linear ODEs with Newton–Picard Method

2021 ◽  
Author(s):  
Florent Bréhard
Keyword(s):  
Picard Method ◽  
Linear Odes

Bases for Second Order Linear ODEs

2020 ◽  
Vol 127 (9) ◽  
pp. 849-849
Author(s):  
Peter McGrath
Keyword(s):  
Second Order ◽  
Order Linear ◽  
Linear Odes

Two-step fourth order methods for linear ODEs of the second order

2008 ◽  
Vol 51 (4) ◽  
pp. 449-460 ◽  
Author(s):  
Mikhail V. Bulatov ◽  
Guido Vanden Berghe
Keyword(s):  
Fourth Order ◽  
Second Order ◽  
Linear Odes

Higher order linear ODEs

2021 ◽  
pp. 59-102
Author(s):  
Suman Kumar Tumuluri
Keyword(s):  
Higher Order ◽  
Order Linear ◽  
Linear Odes

Non-Linear ODEs Of First and Second Order

2007 ◽  
pp. 239-364
Author(s):  
Mircea V. Soare ◽  
Petre P. Teodorescu ◽  
Ileana Toma
Keyword(s):  
Second Order ◽  
Non Linear ◽  
Linear Odes

Multistep Newton–Picard Method for Nonlinear Differential Equations

2020 ◽  
Vol 43 (11) ◽  
pp. 2148-2155
Author(s):  
Yinkun Wang ◽  
Guyan Ni ◽  
Yicheng Liu
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Picard Method

TOPOLOGICAL CHAOS FOR BIRTH-AND-DEATH-TYPE MODELS WITH PROLIFERATION

2002 ◽  
Vol 12 (06) ◽  
pp. 755-775 ◽  
Author(s):  
JACEK BANASIAK ◽  
MIROSŁAW LACHOWICZ
Keyword(s):  
Death Process ◽  
Antineoplastic Drugs ◽  
Birth And Death Process ◽  
Neoplastic Cells ◽  
Cellular Resistance ◽  
Infinite Systems ◽  
Topological Chaos ◽  
Linear Odes ◽  
Different Levels

In this paper we consider a class of infinite systems of linear ODEs. Each system corresponds to a process characterized by two components: the conservative one (birth-and-death process) and the proliferative one. A system of this type can describe the population of neoplastic cells divided into subpopulations characterized by different levels of cellular resistance to antineoplastic drugs. Under suitable assumptions on the "birth" (amplification) coefficients, the "death" (deamplification) coefficients and the averages of the life-spans we prove that this class of models is topologically chaotic.

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