scholarly journals SOLUTION OF SECOND ORDER LINEAR AND NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS USING LEGENDRE OPERATIONAL MATRIX OF DIFFERENTIATION

2014 ◽  
Vol 93 (2) ◽  
Author(s):  
C.Y. Jung ◽  
Z. Liu ◽  
A. Rafiq ◽  
F. Ali ◽  
S.M. Kang
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Operational Matrix ◽  
Second Order ◽  
Nonlinear Ordinary Differential Equations ◽  
Order Linear ◽  
Operational Matrix Of Differentiation ◽  
Linear And Nonlinear

scholarly journals Modified operational matrix method for second-order nonlinear ordinary differential equations with quadratic and cubic terms

2020 ◽  
Vol 10 (2) ◽  
pp. 218-225
Author(s):  
Burcu Gürbüz ◽  
Mehmet Sezer
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Matrix Method ◽  
Laguerre Polynomials ◽  
Operational Matrix ◽  
Second Order ◽  
Nonlinear Ordinary Differential Equations ◽  
Algebraic Equations ◽  
Operational Matrix Method ◽  
The Matrix

In this study, by means of the matrix relations between the Laguerre polynomials, and their derivatives, a novel matrix method based on collocation points is modified and developed for solving a class of second-order nonlinear ordinary differential equations having quadratic and cubic terms, via mixed conditions. The method reduces the solution of the nonlinear equation to the solution of a matrix equation corresponding to system of nonlinear algebraic equations with the unknown Laguerre coefficients. Also, some illustrative examples along with an error analysis based on residual function are included to demonstrate the validity and applicability of the proposed method.

scholarly journals Oscillation criteria for second order differential equations with damping

1990 ◽  
Vol 49 (1) ◽  
pp. 43-54 ◽  
Author(s):  
S. R. Grace
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Nonlinear Ordinary Differential Equations ◽  
Oscillation Criteria ◽  
Second Order Differential Equations ◽  
Linear Differential

AbstractNew oscillation criteria are given for second order nonlinear ordinary differential equations with alternating coefficients. The results involve a condition obtained by Kamenev for linear differential equations. The obtained criterion for superlinear differential equations is a complement of the work established by Kwong and Wong, and Philos, for sublinear differential equations and by Yan for linear differential equations.

Application of He’s Homotopy Perturbation Method to Stiff Systems of Ordinary Differential Equations

2008 ◽  
Vol 63 (1-2) ◽  
pp. 19-23 ◽  
Author(s):  
Mohammad Taghi Darvishi ◽  
Farzad Khani
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Homotopy Perturbation Method ◽  
Nonlinear Ordinary Differential Equations ◽  
Stiff Systems ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear

We propose He’s homotopy perturbation method (HPM) to solve stiff systems of ordinary differential equations. This method is very simple to be implemented. HPM is employed to compute an approximation or analytical solution of the stiff systems of linear and nonlinear ordinary differential equations.

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