On the radius of convergence of the simplest power series solution of Painlevé-I equation

1986 ◽  
Vol 3 (2) ◽  
pp. 281-294 ◽  
Author(s):  
Yoshinori Kametaka ◽  
Matu-Tarow Noda
Keyword(s):  
Power Series ◽  
Series Solution ◽  
Radius Of Convergence ◽  
Power Series Solution

Optimal algebra and power series solution of fractional Black-Scholes pricing model

2021 ◽  
Vol 25 (8) ◽  
pp. 6075-6082
Author(s):  
Hemanta Mandal ◽  
B. Bira ◽  
D. Zeidan
Keyword(s):  
Power Series ◽  
Series Solution ◽  
Power Series Solution ◽  
Pricing Model ◽  
Black Scholes

An analytical solution of the Gibbs–Dehem equation in multicomponent systems

1970 ◽  
Vol 48 (5) ◽  
pp. 752-763 ◽  
Author(s):  
A. D. Pelton
Keyword(s):  
Analytical Solution ◽  
Power Series ◽  
Series Solution ◽  
Power Series Solution ◽  
Multicomponent Systems ◽  
Duhem Equation ◽  
Number Of Components ◽  
Analytical Power

A general analytical power-series solution of the Gibbs–Duhem equation in multicomponent systems of any number of components has been developed. The simplicity and usefulness of the solution is made possible through the choice of a special set of composition variables.

The generalized convective Cahn–Hilliard equation: Symmetry classification, power series solutions and dynamical behavior

2019 ◽  
Vol 31 (02) ◽  
pp. 2050024
Author(s):  
Zhi-Yong Zhang ◽  
Kai-Hua Ma ◽  
Li-Sheng Zhang
Keyword(s):  
Power Series ◽  
Critical Points ◽  
Driving Force ◽  
Series Solution ◽  
Dynamical Behavior ◽  
Compressive Force ◽  
Power Series Solution ◽  
Symmetry Classification ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation

We first perform a complete Lie symmetry classification of the generalized convective Cahn–Hilliard equation. Then using the obtained symmetries, we mainly study the convective Cahn–Hilliard equation, of which a new power series solution is constructed. In particular for the crystal surface growth processes, the truncated series solution shows that the surface structures include peaks and valleys, and can exhibit different evolution trends with the driving force varying from compressive force to tensile force. Moreover, there exist several critical points for the driving force, where the surface configurations take the jump changes and show different features on the both sides of such critical points. According to the effects of driving forces, we analyze the dynamical features of crystal growth.

scholarly journals Matrix-valued Bratu equation and the exact solution of its initial value problem

2020 ◽  
pp. 1950007
Author(s):  
Hiroto Inoue
Keyword(s):  
Exact Solution ◽  
Power Series ◽  
Initial Value Problem ◽  
Series Solution ◽  
Power Series Solution ◽  
Matrix Solution ◽  
Initial Value ◽  
Bratu Equation ◽  
Exponential Matrix

A matrix-valued extension of the Bratu equation is defined. For its initial value problem, the exponential matrix solution and power series solution are provided.

Shear horizontal surface acoustic waves in a magneto-electro-elastic system

2016 ◽  
Vol 25 (1-2) ◽  
pp. 1-13 ◽  
Author(s):  
Shahin Eskandari ◽  
Hossein M. Shodja
Keyword(s):  
Power Series ◽  
Shear Wave ◽  
Half Space ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Acoustic Waves ◽  
Series Solution ◽  
Surface Acoustic Waves ◽  
Power Series Solution ◽  
Shear Horizontal

AbstractPropagation of shear horizontal surface acoustic waves (SHSAWs) within a functionally graded magneto-electro-elastic (FGMEE) half-space was previously presented (Shodja HM, Eskandari S, Eskandari M. J. Eng. Math. 2015, 1–18) In contrast, the current paper considers propagation of SHSAWs in a medium consisting of an FGMEE layer perfectly bonded to a homogeneous MEE substrate. When the FGMEE layer is described by some special inhomogeneity functions – all the MEE properties have the same variation in depth which may or may not be identical to that of the density – we obtain the exact closed-form solution for the MEE fields. Additionally, certain special inhomogeneity functions with monotonically decreasing bulk shear wave velocity in depth are considered, and the associated boundary value problem is solved using power series solution. This problem in the limit as the layer thickness goes to infinity collapses to an FGMEE half-space with decreasing bulk shear wave velocity in depth. It is shown that in such a medium SHSAW does not propagate. Using power series solution we can afford to consider some FGMEE layers of practical importance, where the composition of the MEE obeys a prescribed volume fraction variation. The dispersive behavior of SHSAWs in the presence of such layers is also examined.

Sign in / Sign up

Export Citation Format

Share Document