Innovative iteration technique for nonlinear ordinary differential equations of large deflection problem of circular plates

In the present paper a new linearization technique referred to as the locally transversal linearization (LTL) is used for large deflection analyses of axisymmetric circular plates. The LTL procedure, where solution manifolds of linearized equations are made to intersect transversally those of the nonlinear ordinary differential equations, reduces the given set of nonlinear ordinary differential equations to a set of nonlinear algebraic equations in terms of a descretized set of unknown response vectors.

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SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR SECOND ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS HAVING WEAKLY DISCONTINUOUS REDUCED SOLUTIONS

Acta Mathematica Scientia ◽

10.1016/s0252-9602(18)30303-5 ◽

1988 ◽

Vol 8 (3) ◽

pp. 239-248 ◽

Cited By ~ 2

Author(s):

Weili Zhao

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Boundary Value Problems ◽

Boundary Value ◽

Second Order ◽

Singularly Perturbed ◽

Nonlinear Ordinary Differential Equations

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Impact of double-diffusive convection and motile gyrotactic microorganisms on magnetohydrodynamics bioconvection tangent hyperbolic nanofluid

Open Physics ◽

10.1515/phys-2020-0009 ◽

2020 ◽

Vol 18 (1) ◽

pp. 74-88 ◽

Cited By ~ 1

Author(s):

Tanveer Sajid ◽

Muhammad Sagheer ◽

Shafqat Hussain ◽

Faisal Shahzad

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Transfer Rate ◽

Mass Transfer Rate ◽

Physical Nature ◽

Working Fluid ◽

Nonlinear Ordinary Differential Equations ◽

Gyrotactic Microorganisms ◽

Motile Gyrotactic Microorganisms ◽

Double Diffusive

AbstractThe double-diffusive tangent hyperbolic nanofluid containing motile gyrotactic microorganisms and magnetohydrodynamics past a stretching sheet is examined. By adopting the scaling group of transformation, the governing equations of motion are transformed into a system of nonlinear ordinary differential equations. The Keller box scheme, a finite difference method, has been employed for the solution of the nonlinear ordinary differential equations. The behaviour of the working fluid against various parameters of physical nature has been analyzed through graphs and tables. The behaviour of different physical quantities of interest such as heat transfer rate, density of the motile gyrotactic microorganisms and mass transfer rate is also discussed in the form of tables and graphs. It is found that the modified Dufour parameter has an increasing effect on the temperature profile. The solute profile is observed to decay as a result of an augmentation in the nanofluid Lewis number.

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A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations

Numerical Mathematics Theory Methods and Applications ◽

10.4208/nmtma.2016.m1429 ◽

2016 ◽

Vol 9 (4) ◽

pp. 619-639 ◽

Cited By ~ 3

Author(s):

Zhong-Qing Wang ◽

Jun Mu

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Collocation Method ◽

Initial Value Problems ◽

Numerical Experiments ◽

High Order Accuracy ◽

Nonlinear Ordinary Differential Equations ◽

Initial Value ◽

Order Accuracy ◽

Long Time

AbstractWe introduce a multiple interval Chebyshev-Gauss-Lobatto spectral collocation method for the initial value problems of the nonlinear ordinary differential equations (ODES). This method is easy to implement and possesses the high order accuracy. In addition, it is very stable and suitable for long time calculations. We also obtain thehp-version bound on the numerical error of the multiple interval collocation method underH1-norm. Numerical experiments confirm the theoretical expectations.

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