scholarly journals A Modified Solution of the Nonlinear Singular Oscillator by Extended Iteration Procedure

2019 ◽  
pp. 1-9
Author(s):  
B. M. Ikramul Haque ◽  
M. M. Ayub Hossain
Keyword(s):  
Fourier Series ◽  
Analytic Solution ◽  
Rate Of Change ◽  
Iteration Procedure ◽  
Approximate Analytic Solution ◽  
Modified Technique ◽  
The Third ◽  
Present Technique ◽  
Approximate Frequency ◽  
Good Agreement

A modified solution of the nonlinear singular oscillator has been obtained based on the extended iteration procedure. We have used an appropriate truncation of the obtained Fourier series in each step of iterations to determine the approximate analytic solution of the oscillator. The third approximate frequency of the nonlinear singular oscillator shows a good agreement with its exact values. Earlier different authors presented the analytic solution of the oscillator by using various types of methods. We have compared the results obtained by the modified technique with some of the existing results. We see that some of their techniques deviate from higher-order approximations and the present technique performs comparatively better.  The rate of change of percentage of error of the presented modified solution shows the validity of convergence.

scholarly journals On the Analytical Approximation of the Nonlinear Cubic Oscillator by an Iteration Method

2019 ◽  
pp. 1-9
Author(s):  
B. M. Ikramul Haque ◽  
A. K. M. Selim Reza ◽  
Md. Mominur Rahman
Keyword(s):  
Nonlinear Oscillator ◽  
Analytic Solution ◽  
Analytical Approximation ◽  
Approximate Analytic Solution ◽  
Rapid Convergence ◽  
Modified Technique ◽  
Validity Range ◽  
Approximate Frequency ◽  
Truncated Fourier Series ◽  
Good Agreement

A modified approximate analytic solution of the cubic nonlinear oscillator “ ” has been obtained based on an iteration procedure. Here we have used the truncated Fourier series in each iterative step. The approximate frequencies obtained by this technique show a good agreement with the exact frequency. The percentage of error between exact frequency and our fifth approximate frequency is as low as 0.009%. The calculation with this technique is very easy. This easily-calculated modified technique accelerates the rapid convergence, reduces the error and increases the validity range of the solution.

A shallow-water sloshing model for wave breaking in rectangular tanks

2014 ◽  
Vol 746 ◽  
pp. 437-465 ◽  
Author(s):  
Matteo Antuono ◽  
Andrea Bardazzi ◽  
Claudio Lugni ◽  
Maurizio Brocchini
Keyword(s):  
Shallow Water ◽  
Wave Breaking ◽  
Analytic Solution ◽  
Turbulent Viscosity ◽  
Approximate Analytic Solution ◽  
Experimental Campaign ◽  
Proposed Model ◽  
Water Conditions ◽  
Reliability And Robustness ◽  
Good Agreement

AbstractWe propose a simple, robust and efficient sloshing model that accounts for breaking phenomena evolving in rectangular tanks and in shallow-water conditions. The model has been obtained by applying Fourier analysis to Boussinesq-type equations and using an approximate analytic solution for the vorticity generated by wave breaking. The toe of the breaker and the intensity of the vorticity injected at the free surface are computed on the basis of literature results for coastal-type breakers. A first experimental campaign has been used to calibrate the turbulent viscosity of the sloshing model, while a second campaign has been run as final validation. The overall good agreement between the numerical outputs and the experimental data confirms the reliability and robustness of the proposed model.

scholarly journals A SOLITARY CONVERGENT PERIODIC SOLUTION OF THE INVERSE TRULY NONLINEAR OSCILLATOR BY MODIFIED MICKENS’ EXTENDED ITERATION PROCEDURE

2021 ◽  
Vol 16 (8) ◽  
Author(s):  
M. M. Ayub Hossain
Keyword(s):  
Information Technology ◽  
Periodic Solution ◽  
Fourier Series ◽  
Computer Science ◽  
Nonlinear Oscillator ◽  
Exact Result ◽  
Iteration Procedure ◽  
Strongly Nonlinear ◽  
Present Technique ◽  
Science Information

The inverse truly nonlinear oscillator is the most applied in the field of computer science, information technology, physics, electrical engineering, and mechanical engineering. The solution of the inverse truly nonlinear oscillator has been obtained by modified Mickens’ extended iteration procedure. To determine the solution of the oscillator a special type of Fourier series has been used. The iterated solutions are convergent as the second, third, and fourth approximate frequencies of the oscillator show a good concurrence with the exact result. Some researchers presented the solutions of the same oscillator by applying different methods. We have compared the obtained results with some previously published results. Some of their techniques diverge at higher-order stages but the present technique is convergent there. The method is mainly illustrated in the strongly nonlinear inverse oscillator, but it can be widely applicable in other problems arising from nonlinear sciences and engineering.

scholarly journals An approximate analytic solution of a particular boundary value problem

2001 ◽  
Vol 27 (8) ◽  
pp. 513-520
Author(s):  
Ugur Tanriver ◽  
Aravinda Kar
Keyword(s):  
Boundary Value Problem ◽  
Heat Conduction Equation ◽  
Analytic Solution ◽  
Boundary Value ◽  
Three Dimensional ◽  
Welding Process ◽  
Approximate Analytic Solution ◽  
Analytic Expression ◽  
Steady State Heat ◽  
Laser Welding Process

This note is concerned with the three-dimensional quasi-steady-state heat conduction equation subject to certain boundary conditions in the wholex′y′-plane and finite inz′-direction. This type of boundary value problem arises in laser welding process. The solution to this problem can be represented by an integral using Fourier analysis. This integral is approximated to obtain a simple analytic expression for the temperature distribution.

New Developments for the Description of Oil Leakages by Advective Migration From Submarine Pipelines

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Renan Martins Baptista ◽  
Ricardo Antonio Francisco Machado ◽  
Marintho Bastos Quadri ◽  
Ariovaldo Bolzan ◽  
André Lourenço Nogueira ◽  
...  
Keyword(s):  
Horizontal Plane ◽  
Immiscible Displacement ◽  
Preliminary Evaluation ◽  
Leakage Detection ◽  
New Developments ◽  
Gravitational Flow ◽  
The Third ◽  
Alternative Approach ◽  
High Standards ◽  
Good Agreement

The significant growth in offshore operations increases the risk of a pipeline rupture, even considering the high standards of safety involved. Throughout a submarine leakage, four different amounts of oil may be accounted. The first one is the oil volume released until the leakage detection. The second one is the volume leaked throughout mitigation initiatives (e.g., pump shutdown and valve closure). The third parcel is the amount released by gravitational flow. Finally, the fourth and last amount of oil is released due to the water-oil entrainment, generally known as advective migration. Normally, a considerable amount of oil is released in this step. It begins just after the internal pipeline pressure becomes equal to the external one. The present work continues to introduce a mathematical alternative approach, based on the theories of perturbation and unstable immiscible displacement, to accurately estimate the leakage kinetics and the amount of oil released by the advective migration phenomenon. Situations considering different hole sizes and thicknesses were tested experimentally and through simulations. Additional experiments were accomplished using smooth and rough edge surfaces, besides different slopes (using the horizontal plane as reference). Those experiments permitted a preliminary evaluation of the importance of these factors. The results obtained with the model showed good agreement with the experimental data in many situations considered.

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