Solution of a boundary-value problem for a nonlinear differential equation by the method of successive approximations

1974 ◽  
Vol 26 (3) ◽  
pp. 380-383
Author(s):  
S. I. Prokopets
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Nonlinear Differential Equation ◽  
Boundary Value ◽  
Successive Approximations ◽  
Method Of Successive Approximations

Interaction of acoustic waves with moving boundary surfaces

2021 ◽  
pp. 59-60
Author(s):  
Keyword(s):  
Boundary Value Problem ◽  
Acoustic Waves ◽  
Moving Boundary ◽  
Boundary Value ◽  
Boundary Surface ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Ultrasonic Beam ◽  
Static Approximation ◽  
Quasi Static Approximation

A quasi-static approximation is considered for the interaction of a probing ultrasonic beam with a vibrating boundary surface. The model is considered in the form of a boundary value problem, presented in the form of d'Alembert. The method of successive approximations was used for the solution. The error arising from this interaction is established. Keywords: quasi-static approximation, boundary value problem, d'Alembert form, Doppler effect, rheological medium. [email protected]; [email protected]

A priori estimates of the positive solution of the two-point boundary value problem for one second-order nonlinear differential equation

2019 ◽  
pp. 38-48
Author(s):  
Edelkhan Abduragimov
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Nonlinear Differential Equation ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Second Order ◽  
Point Boundary ◽  
Priori Estimates

A priori estimates of the positive solution of the two-point boundary value problem are obtained $y^{\prime\prime}=-f(x,y)$, $0<x<1$, $y(0)=y(1)=0$ assuming that $f(x,y)$ is continuous at $x \in [0,1]$, $y \in R$ and satisfies the condition $a_0 x^{\gamma}y^p \leq f(x,y) \leq a_1 y^p$, where $a_0>0$, $a_1>0$, $p>1$, $\gamma \geq 0$ -- constants.

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