Phase portraits for some symmetric Riccati cubic polynomial differential equations
نویسندگان
چکیده
منابع مشابه
global results on some nonlinear partial differential equations for direct and inverse problems
در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
GIP integrators for Matrix Riccati Differential Equations
Matrix Riccati Differential Equations (MRDEs) are initial value problems of the form: X 0 1⁄4 A21 XA11 þ A22X XA12X; Xð0Þ 1⁄4 X0: These equations arise frequently throughout applied mathematics, science, and engineering. It can happen that even when the Aij are smooth functions of t or constant, the solution X may have a singularity or even infinitely many singularities. This paper shows severa...
متن کاملSymmetric matrix polynomial equations
For problems of linear control system synthesis, an apparatus of polynomial equations (for single-variable case) and of matrix polynomial equations (for multivariable case) was successfully developed in recent times, cf. [1]. In connection with quadratic criteria, we are led to equations of special type, containing an operation of conjugation ah-* a* representing a(s) i-> a( — s) for continuous...
متن کاملGlobal phase Portraits of some Reversible cubic Centers with Noncollinear singularities
The results in this paper show that the cubic vector fields ẋ = −y + M(x, y) − y(x + y), ẏ = x + N(x, y) + x(x + y), where M,N are quadratic homogeneous polynomials, having simultaneously a center at the origin and at infinity, have at least 61 and at most 68 topologically different phase portraits. To this end the reversible subfamily defined by M(x, y) = −γxy, N(x, y) = (γ − λ)x + αλy with α,...
متن کاملConvergence analysis of spectral Tau method for fractional Riccati differential equations
In this paper, a spectral Tau method for solving fractional Riccati differential equations is considered. This technique describes converting of a given fractional Riccati differential equation to a system of nonlinear algebraic equations by using some simple matrices. We use fractional derivatives in the Caputo form. Convergence analysis of the proposed method is given an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2018
ISSN: 0166-8641
DOI: 10.1016/j.topol.2017.11.023