scholarly journals An Efficient Method for Solving System of Third-Order Nonlinear Boundary Value Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Muhammad Noor ◽  
Khalida Noor ◽  
Asif Waheed ◽  
Eisa A. Al-Said
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Contact Problems ◽  
Convergent Series ◽  
Nonlinear Boundary Value Problems ◽  
Third Order ◽  
Variation Of Parameters ◽  
Suggested Technique ◽  
Nonlinear Boundary Value

we use the modified variation of parameters method for finding the analytical solution of a system of third-order nonlinear boundary value problems associated with obstacle, unilateral, and contact problems. The results are calculated in terms of convergent series with easily computable components. The suggested technique is applied without any discretization, perturbation, transformation, and restrictive assumptions. Moreover, it is free from round off errors. Some examples are given to illustrate the implementation and efficiency of the modified variation of parameters method.

scholarly journals Comparison of the method of variation of parameters to semi-analytical methods for solving nonlinear boundary value problems in engineering

2019 ◽  
Vol 9 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Travis J. Moore ◽  
Vedat S. Ertürk
Keyword(s):  
Numerical Methods ◽  
Boundary Value Problems ◽  
Analytical Methods ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Engineering Applications ◽  
Concentrated Load ◽  
Variation Of Parameters ◽  
Nonlinear Boundary Value

AbstractSolutions to nonlinear boundary value problems modelling physical phenomena in engineering applications have traditionally been approximated using numerical methods. More recently, several semi-analytical methods have been developed and used extensively in diverse engineering applications. This work compares the method of variation of parameters to semi-analytical methods for solving nonlinear boundary value problems arising in engineering. The accuracy and efficiency of the method of variation of parameters are compared to those of two widely used semi-analytical methods, the Adomian decomposition method and the differential transformation method, for three practical engineering boundary value problems: (1) the deflection of a cantilevered beam with a concentrated load, (2) an adiabatic tubular chemical reactor which processes an irreversible exothermal reaction, and (3) the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylinder conduit. The accuracy and convergence of each method is investigated using the error remainder function. The method of variation of parameters is significantly more efficient than both the semi-analytical methods and traditional numerical methods while maintaining comparable accuracy. Unlike the semi-analytical methods, the efficiency of variation of parameters is independent of the nonlinearity. Variation of parameters is shown to be an attractive alternative to semi-analytical methods and traditional numerical methods for solving boundary value problems encountered in engineering applications in which solution efficiency is important.

ON FUČIK SPECTRA FOR THIRD ORDER EQUATIONS

2007 ◽  
Vol 12 (2) ◽  
pp. 227-234 ◽  
Author(s):  
Natalija Sergejeva
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Third Order ◽  
Fučík Spectrum ◽  
Fučik Spectrum ◽  
Nonlinear Boundary Value ◽  
Fucik Spectrum

We construct the Fučik spectrum for some third order nonlinear boundary value problems. This spectrum differs essentially from the known Fučik spectra.

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