Modification of Galerkin's method for a boundary problem of an ordinary nonlinear differential equation

1982 ◽  
Vol 33 (5) ◽  
pp. 455-460
Author(s):  
�. I. Kucherenko
Keyword(s):  
Differential Equation ◽  
Boundary Problem ◽  
Nonlinear Differential Equation ◽  
Galerkin’S Method ◽  
Ordinary Nonlinear Differential Equation ◽  
Galerkin's Method

scholarly journals The Combined RKM and ADM for Solving Nonlinear Weakly Singular Volterra Integrodifferential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Xueqin Lv ◽  
Sixing Shi
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Efficient Method ◽  
Reproducing Kernel ◽  
Numerical Solutions ◽  
Adomian Decomposition Method ◽  
Integrodifferential Equations ◽  
Ordinary Nonlinear Differential Equation ◽  
Weakly Singular ◽  
Adomian Decomposition

The reproducing kernel method (RKM) and the Adomian decomposition method (ADM) are applied to solventh-order nonlinear weakly singular Volterra integrodifferential equations. The numerical solutions of this class of equations have been a difficult topic to analyze. The aim of this paper is to use Taylor’s approximation and then transform the givennth-order nonlinear Volterra integrodifferential equation into an ordinary nonlinear differential equation. Using the RKM and ADM to solve ordinary nonlinear differential equation is an accurate and efficient method. Some examples indicate that this method is an efficient method to solventh-order nonlinear Volterra integro-differential equations.

Buckling of Sandwich Cylinders Under Combined Compression, Torsion, and Bending Loads

1955 ◽  
Vol 22 (3) ◽  
pp. 324-328
Author(s):  
C. T. Wang ◽  
R. J. Vaccaro ◽  
D. F. De Santo
Keyword(s):  
Differential Equation ◽  
Axial Compression ◽  
Theoretical Investigation ◽  
Critical Loads ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Governing Differential Equation ◽  
Bending Loads ◽  
Interaction Curves

Abstract A theoretical investigation is carried out on the buckling of sandwich cylinders under combined compression, torsion, and bending loads. The governing differential equation is solved by using Galerkin’s method. The interrelationship obtained between the critical loads is plotted in the form of nondimensional interaction curves. In the limiting cases of axial compression alone, torsion alone, bending alone, and combined bending and axial compression, the results agree with those obtained previously (1–3).

Steady-state modelling method for matrix-reactance frequency converter with boost topology

2011 ◽  
Vol 60 (2) ◽  
pp. 137-148
Author(s):  
Igor Korotyeyev ◽  
Beata Zięba
Keyword(s):  
Fourier Series ◽  
Steady State ◽  
Differential Equations ◽  
Numerical Method ◽  
Frequency Converter ◽  
Double Fourier Series ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Modelling Method ◽  
Three Phase

Steady-state modelling method for matrix-reactance frequency converter with boost topologyThis paper presents a method intended for calculation of steady-state processes in AC/AC three-phase converters that are described by nonstationary periodical differential equations. The method is based on the extension of nonstationary differential equations and the use of Galerkin's method. The results of calculations are presented in the form of a double Fourier series. As an example, a three-phase matrix-reactance frequency converter (MRFC) with boost topology is considered and the results of computation are compared with a numerical method.

scholarly journals Oscillatory behavior of a second order nonlinear advanced differential equation with mixed neutral terms

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hongwei Shi ◽  
Yuzhen Bai
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Oscillation Criteria ◽  
Order Nonlinear Differential Equation

AbstractIn this paper, we present several new oscillation criteria for a second order nonlinear differential equation with mixed neutral terms of the form $$ \bigl(r(t) \bigl(z'(t)\bigr)^{\alpha }\bigr)'+q(t)x^{\beta } \bigl(\sigma (t)\bigr)=0,\quad t\geq t_{0}, $$(r(t)(z′(t))α)′+q(t)xβ(σ(t))=0,t≥t0, where $z(t)=x(t)+p_{1}(t)x(\tau (t))+p_{2}(t)x(\lambda (t))$z(t)=x(t)+p1(t)x(τ(t))+p2(t)x(λ(t)) and α, β are ratios of two positive odd integers. Our results improve and complement some well-known results which were published recently in the literature. Two examples are given to illustrate the efficiency of our results.

Galerkin’s method revisited and corrected in the problem of Jaworski and Dowell

2021 ◽  
Vol 155 ◽  
pp. 107604
Author(s):  
Isaac Elishakoff ◽  
Marco Amato ◽  
Alessandro Marzani
Keyword(s):  
Galerkin’S Method ◽  
Galerkin's Method
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