Influence functions for usual fourth-order homogeneous linear ordinary differential equations

2001 ◽  
Vol 215 (4) ◽  
pp. 219-224
Author(s):  
Y S Zhang
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Influence Functions ◽  
Linear Ordinary Differential Equations ◽  
Homogeneous Linear

scholarly journals Diagonally Implicit Runge-Kutta Fourth Order Four-Stage Method for Linear Ordinary Differential Equations with Minimized Error Norm

2014 ◽  
Vol 5 (1) ◽  
Author(s):  
Nur Izzati Che Jawias ◽  
Fudziah Ismail ◽  
Mohamed Suleiman ◽  
Azmi Jaafar
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
New Method ◽  
Test Problems ◽  
Error Norm ◽  
Linear Ordinary Differential Equations ◽  
Free Parameters ◽  
Runge Kutta ◽  
Order Four

We constructed a new fourth order four-stage diagonally implicit Runge-Kutta (DIRK) method which is specially designed for the integrations of linear ordinary differential equations (LODEs). The method is obtained based on theButcher’s error equations. In the derivation, the error norm is minimized so that the free parameters chosen are obtained from the minimized error norm. Row simplifying assumption is also used so that the number of equations forthe method can be reduced and simplified. A set of test problems are used to validate the method and numerical results show that the new method is more efficient in terms of accuracy compared to the existing method.

scholarly journals Two non-elementary integral functions defined using central factorial powers

2015 ◽  
Vol 23 ◽  
pp. 98
Author(s):  
T.P. Goy
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Variable Coefficients ◽  
Elementary Functions ◽  
Order Linear ◽  
Linear Ordinary Differential Equations

We study two new real-valued non-elementary functions generated by central factorial powers. Graphs of such functions are plotted and some of their properties are proved. It is also shown that new integral functions are solutions of fourth order linear ordinary differential equations with variable coefficients.

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