scholarly journals On Fast Spectral Solving Triharmonic Equation with Simply Supported Type Condition

2018 ◽  
Author(s):  
Agah D. Garnadi
Keyword(s):  
Boundary Value Problem ◽  
Spectral Method ◽  
Boundary Value ◽  
Type Condition ◽  
Simply Supported

This note is addressed to fast solving simply supported boundary value problem oftriharmonic equation in the unit rectangle using spectral method.

scholarly journals On Fast Solving Spectral Method to Biharmonic Equation Of the Second Kind

2018 ◽  
Author(s):  
Agah D. Garnadi
Keyword(s):  
Boundary Value Problem ◽  
Spectral Method ◽  
Biharmonic Equation ◽  
Boundary Value ◽  
Simply Supported

This note is addressed to fast solving simply supported boundary value problem ofbiharmonic equation in the unit rectangle.

scholarly journals A Boundary Value Problem with Multivariables Integral Type Condition for Parabolic Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-13
Author(s):  
A. L. Marhoune ◽  
F. Lakhal
Keyword(s):  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Continuous Dependence ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Analysis Method ◽  
Type Condition ◽  
Integral Type ◽  
Priori Estimates

We study a boundary value problem with multivariables integral type condition for a class of parabolic equations. We prove the existence, uniqueness, and continuous dependence of the solution upon the data in the functional wieghted Sobolev spaces. Results are obtained by using a functional analysis method based on two-sided a priori estimates and on the density of the range of the linear operator generated by the considered problem.

scholarly journals Evaluation of Scipy.ode Integrators in Solving the Lane-Emden Equation for Polytropes as a Boundary Value Problem with a Fitting Method

2017 ◽  
Vol 16 (1) ◽  
pp. 67-80
Author(s):  
M N Anandaram
Keyword(s):  
Boundary Value Problem ◽  
Spectral Method ◽  
Boundary Value ◽  
Reference Value ◽  
Emden Equation ◽  
Acceptable Accuracy ◽  
Fitting Method ◽  
Chebyshev Spectral Method

The use of Scipy integrators like dopri5 and others in accurately solving the  Lane-Emden equation of a polytrope as a two-point BVP with fitting is investigated by comparing the Emden radius with the extended precision reference value obtained by Boyd's Chebyshev spectral method. It is found that both dopri5 and dop853 integrators provide acceptable accuracy upto 14 decimal digits.

A Class of Minimum Weight Shafts

1974 ◽  
Vol 96 (1) ◽  
pp. 166-170 ◽  
Author(s):  
C. J. Maday
Keyword(s):  
Boundary Value Problem ◽  
Critical Speed ◽  
Minimum Weight ◽  
Boundary Value ◽  
Minimum Principle ◽  
Light Weight ◽  
Point Boundary ◽  
Simply Supported ◽  
Set Up

Light weight shafts reduce bearing forces and allow the use of smaller bearings, seals, and supports. The Minimum Principle is used to set up the problem of determining the minimum weight shaft for a specified critical speed of given order. Specific examples include simply supported shafts and cantilevered shafts with and without a disk. The designs are obtained from the solution to a nonlinear multi-point boundary-value-problem. Minimum weight configurations represent a standard against which other designs, such as stepped shafts, can be compared.

scholarly journals Analysis of natural frequency of flexural vibrations of a single-span beam with the consideration of Timoshenko effect

2018 ◽  
Vol 3 (21) ◽  
pp. 215-232
Author(s):  
Jerzy Jaroszewicz ◽  
Krzysztof Łukaszewicz
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Boundary Value ◽  
Rotational Inertia ◽  
Cauchy Function ◽  
Simply Supported Beam ◽  
Good Convergence ◽  
Simply Supported ◽  
Elastic Characteristics

This paper presents general solution of boundary value problem for constant cross-section Timoshenko beams with four typical boundary conditions. The authors have taken into consideration rotational inertia and shear strain by using the theory of influence by Cauchy function and characteristic series. The boundary value problem of transverse vibration has been formulated and solved. The characteristic equations considering the exact bending theory have been obtained for four cases: the clamped boundary conditions; a simply supported beam and clamped on the other side; a simply supported beam; a cantilever beam. The obtained estimators of fundamental natural frequency take into account mass and elastic characteristics of beams and Timoshenko effect. The results of calculations prove high convergence of the estimators to the exact values which were calculated by Timoshenko who used Bessel functions. Characteristic series having an alternating sign power series show good convergence. As it is shown in the paper, the error lower than 5% was obtained after taking into account only two first significant terms of the series. It was proved that neglecting the Timoshenko effect in case of short beams of rectangular section with the ratio of their length to their height equal 6 leads to the errors of calculated natural frequency: 5%÷12%.

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