Existence and uniqueness results for a second order differential equation for the ocean flow in arctic gyres

2020 ◽  
Vol 193 (1) ◽  
pp. 177-192 ◽  
Author(s):  
Wenlin Zhang ◽  
JinRong Wang ◽  
Michal Fečkan
Keyword(s):  
Differential Equation ◽  
Existence And Uniqueness ◽  
Order Differential Equation ◽  
Second Order ◽  
Existence And Uniqueness Results ◽  
Second Order Differential Equation ◽  
Uniqueness Results

Existence and Uniqueness Results for Nonlinear Differential Equation Arising in Non-Newtonian Fluid Flow

2000 ◽  
Author(s):  
K. Vajravelu ◽  
J. R. Cannon ◽  
D. Rollins
Keyword(s):  
Differential Equation ◽  
Fluid Flow ◽  
Existence And Uniqueness ◽  
Order Differential Equation ◽  
Perturbation Technique ◽  
Integral Form ◽  
Rotating Cylinder ◽  
Exact Analytical Solutions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

Abstract Solution for a nonlinear second order differential equation, arising in a viscoelastic fluid flow at a rotating cylinder, is obtained. Furthermore, using the Shauder theory and the perturbation technique existence, uniqueness and analyticity results are established. Moreover, the exact analytical solutions (in integral form) are compared with the corresponding numerical ones.

A mechanical method for the solution of second-order linear differential equations

1931 ◽  
Vol 27 (4) ◽  
pp. 546-552 ◽  
Author(s):  
E. C. Bullard ◽  
P. B. Moon
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Order Differential Equation ◽  
Second Order ◽  
Linear Differential Equations ◽  
Mechanical Method ◽  
Order Linear ◽  
Second Order Differential Equation ◽  
Linear Differential

A mechanical method of integrating a second-order differential equation, with any boundary conditions, is described and its applications are discussed.

scholarly journals Periodic solutions for periodic second-order differential equations with variable potentials

2018 ◽  
Vol 24 (2) ◽  
pp. 127-137
Author(s):  
Jaume Llibre ◽  
Ammar Makhlouf
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Second Order Differential Equation ◽  
Existence Of Periodic Solutions

Abstract We provide sufficient conditions for the existence of periodic solutions of the second-order differential equation with variable potentials {-(px^{\prime})^{\prime}(t)-r(t)p(t)x^{\prime}(t)+q(t)x(t)=f(t,x(t))} , where the functions {p(t)>0} , {q(t)} , {r(t)} and {f(t,x)} are {\mathcal{C}^{2}} and T-periodic in the variable t.

Numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument

2017 ◽  
Vol 23 (2) ◽  
Author(s):  
Muhad H. Abregov ◽  
Vladimir Z. Kanchukoev ◽  
Maryana A. Shardanova
Keyword(s):  
Differential Equation ◽  
Numerical Methods ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Deviating Argument ◽  
Second Order Differential Equation

AbstractThis work is devoted to the numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument in minor terms. The sufficient conditions of the one-valued solvability are established, and the a priori estimate of the solution is obtained. For the numerical solution, the problem studied is reduced to the equivalent boundary value problem for an ordinary linear differential equation of fourth order, for which the finite-difference scheme of second-order approximation was built. The convergence of this scheme to the exact solution is shown under certain conditions of the solvability of the initial problem. To solve the finite-difference problem, the method of five-point marching of schemes is used.

Sign in / Sign up

Export Citation Format

Share Document