scholarly journals Fourth-order explicit hybrid method for solving special second-order ordinary differential equations

2013 ◽  
Author(s):  
Faieza Samat ◽  
Fudziah Ismail
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Hybrid Method ◽  
Second Order

scholarly journals A Four-Stage Fifth-Order Trigonometrically Fitted Semi-Implicit Hybrid Method for Solving Second-Order Delay Differential Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Sufia Zulfa Ahmad ◽  
Fudziah Ismail ◽  
Norazak Senu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Hybrid Method ◽  
Delay Differential Equations ◽  
Scientific Literature ◽  
Second Order ◽  
New Method ◽  
Implicit Methods ◽  
Delay Differential ◽  
Fifth Order

We derived a two-step, four-stage, and fifth-order semi-implicit hybrid method which can be used for solving special second-order ordinary differential equations. The method is then trigonometrically fitted so that it is suitable for solving problems which are oscillatory in nature. The methods are then used for solving oscillatory delay differential equations. Numerical results clearly show the efficiency of the new method when compared to the existing explicit and implicit methods in the scientific literature.

scholarly journals A Note on the Integration of Scalar Fourth-Order Ordinary Differential Equations with Four-Dimensional Symmetry Algebras

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Said Waqas Shah ◽  
F. M. Mahomed ◽  
H. Azad
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Second Order ◽  
Two Dimensional ◽  
Lie Point Symmetries ◽  
Complete Integration ◽  
Symmetry Algebras

The complete integration of scalar fourth-order ODEs with four-dimensional symmetry algebras is performed by utilizing Lie’s method which was invoked to integrate scalar second-order ODEs admitting two-dimensional symmetry algebras. We obtain a complete integration of all scalar fourth-order ODEs that possess four Lie point symmetries.

scholarly journals Modified Hybrid Method with Four Stages for Second Order Ordinary Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1028
Author(s):  
Faieza Samat ◽  
Eddie Shahril Ismail
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Hybrid Method ◽  
Hybrid Methods ◽  
High Accuracy ◽  
Parameter Selection ◽  
Second Order ◽  
Duffing Equation ◽  
Numerical Comparisons ◽  
Phase Properties

A modified explicit hybrid method with four stages is presented, with the first stage exactly integrating exp(wx), while the remaining stages exactly integrate sin(wx) and cos(wx). Special attention is paid to the phase properties of the method during the process of parameter selection. Numerical comparisons of the proposed and existing hybrid methods for several second-order problems show that the proposed method gives high accuracy in solving the Duffing equation and Kramarz’s system.

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