scholarly journals On the Legendre differential equation with uncertainties at the regular‐singular point 1: L p ( Ω ) random power series solution and approximation of its statistical moments

2019 ◽  
Vol 1 (4) ◽  
Author(s):  
J. Calatayud ◽  
J.‐C. Cortés ◽  
M. Jornet
Keyword(s):  
Differential Equation ◽  
Singular Point ◽  
Power Series ◽  
Series Solution ◽  
Statistical Moments ◽  
Power Series Solution ◽  
Regular Singular Point ◽  
Random Power Series

Global solutions of linear ordinary differential equations with polynomial coefficients

1975 ◽  
Vol 344 (1636) ◽  
pp. 51-64 ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Power Series ◽  
Series Solution ◽  
Global Solutions ◽  
Linear Ordinary Differential Equation ◽  
Power Series Solution ◽  
Constructive Approach ◽  
Linear Ordinary Differential Equations ◽  
Polynomial Coefficients

A constructive approach is given, closely based on the work of Ford (1936) for continuing analytically a power series solution of a linear ordinary differential equation with polynomial coefficients outside the circle of convergence.

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.

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