scholarly journals A theorem on energy integrals for linear second-order ordinary differential equations with variable coefficients

2016 ◽  
Vol 51 ◽  
pp. 8-12 ◽  
Author(s):  
Leonardo Casetta
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Variable Coefficients ◽  
Second Order ◽  
Energy Integrals

scholarly journals A Singularly P-Stable Multi-Derivative Predictor Method for the Numerical Solution of Second-Order Ordinary Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 806
Author(s):  
Ali Shokri ◽  
Beny Neta ◽  
Mohammad Mehdizadeh Khalsaraei ◽  
Mohammad Mehdi Rashidi ◽  
Hamid Mohammad-Sedighi
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Stability Property ◽  
Stability Region ◽  
Mathieu Equation ◽  
Variable Coefficients ◽  
Second Order ◽  
Implicit Schemes ◽  
The Stability

In this paper, a symmetric eight-step predictor method (explicit) of 10th order is presented for the numerical integration of IVPs of second-order ordinary differential equations. This scheme has variable coefficients and can be used as a predictor stage for other implicit schemes. First, we showed the singular P-stability property of the new method, both algebraically and by plotting the stability region. Then, having applied it to well-known problems like Mathieu equation, we showed the advantage of the proposed method in terms of efficiency and consistency over other methods with the same order.

scholarly journals The Complete Solution of some Kinds of Linear Third Order Partial Differential Equations with Three Independent Variables and variable coefficients

2016 ◽  
Vol 12 (10) ◽  
pp. 6705-6713
Author(s):  
Rusul Hassan Naser ◽  
Wafaa Hadi Hanoon ◽  
Layla Abd Al-Jaleel Mohsin
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Complete Solution ◽  
Variable Coefficients ◽  
Second Order ◽  
Third Order ◽  
Partial Differential ◽  
Independent Variables

In this paper we find the complete solution of some kinds of linear third order partial differential equations of variable coefficients with three independent variables which have the general form  Where A,B,…,T are variable coefficients . By use the some assumptions will transform the above equation to thenonlinear second order ordinary differential equations

scholarly journals New integral functions generated by rising factorial powers

2013 ◽  
Vol 5 (2) ◽  
pp. 217-224
Author(s):  
T.P. Goy ◽  
R.A. Zatorsky
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Variable Coefficients ◽  
Second Order

We consider new nonelementary functions such as the Fresnel integrals, generated by rising factorial powers. Graphs of such functions are plotted and some of their properties are proved. It is shown, that new integral functions are solutions of second order ordinary differential equations with variable coefficients.

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