Solving nonlinear differential equations in astrophysics and fluid mechanics using the generalized pseudospectral method

SeMA Journal ◽  
2021 ◽  
Author(s):  
Mehdi Delkhosh ◽  
Amanj Rahmanzadeh ◽  
Seyyedeh-Fatemeh Shafiei
Keyword(s):  
Differential Equations ◽  
Fluid Mechanics ◽  
Nonlinear Differential Equations ◽  
Pseudospectral Method ◽  
Generalized Pseudospectral Method

Research on Fluid Mechanics with Slip Flow of Viscoelastic Fluid in the Micro Channel

2013 ◽  
Vol 387 ◽  
pp. 51-54
Author(s):  
Zheng Liu ◽  
Jing Zhu ◽  
Lian Cun Zheng
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Fluid Mechanics ◽  
Applied Mathematics ◽  
Nonlinear Differential Equations ◽  
Slip Flow ◽  
Fluid Motion ◽  
Physical Factors ◽  
Stagnation Region ◽  
Analytical Approximations

Stagnation flow, an import research branch of fluid mechanics, describing the fluid motion near the stagnation region, exists on all solid bodies moving in a fluid. And stagnation point boundary layer flow problems described by partial differential equations have attracted many scholars attention nowadays. These problems have become difficult and hot in the study of applied mathematics, mechanics and materials engineering. This paper has transformed the governing boundary layer equations into a system of nonlinear differential equations through the similarity transformation, and the analytical approximations of solutions are derived by homotopy analysis method (HAM). In addition, the effects of physical factors (such as the slip parameter, Magnetic field parameter and Reynolds number) on the flow are examed and discussed graphically. They have a great impact on the speed.

Nonlinear Dynamics, Chaos, and Mechanics

1990 ◽  
Vol 43 (5S) ◽  
pp. S23-S39 ◽  
Author(s):  
Philip Holmes
Keyword(s):  
Nonlinear Dynamics ◽  
Differential Equations ◽  
Fluid Mechanics ◽  
Chaos Theory ◽  
Nonlinear Differential Equations ◽  
Analytical Approaches

Nonlinear Dynamics or “Chaos Theory” is an ill-defined but energetic and rapidly developing subject which cuts across the boundaries of traditional disciplines. In this review, I describe a small part of it: some of the analytical approaches to nonlinear differential equations which have been developed in the last ten to fifteen years. I illustrate them with applications in solid and fluid mechanics.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

scholarly journals Solving nonlinear differential equations with differentiable quantum circuits

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Oleksandr Kyriienko ◽  
Annie E. Paine ◽  
Vincent E. Elfving
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Quantum Circuits

scholarly journals Nonlinear Differential Equations Modeling the Antarctic Circumpolar Current

2021 ◽  
Vol 23 (4) ◽  
Author(s):  
Jifeng Chu ◽  
Kateryna Marynets
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Topological Degree ◽  
Antarctic Circumpolar Current ◽  
Fixed Point Theorems ◽  
Nonlinear Differential Equations ◽  
Existence Results ◽  
Circumpolar Current ◽  
The Antarctic

AbstractThe aim of this paper is to study one class of nonlinear differential equations, which model the Antarctic circumpolar current. We prove the existence results for such equations related to the geophysical relevant boundary conditions. First, based on the weighted eigenvalues and the theory of topological degree, we study the semilinear case. Secondly, the existence results for the sublinear and superlinear cases are proved by fixed point theorems.

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