Hojman's theorem of the third-order ordinary differential equation

2009 ◽  
Vol 18 (8) ◽  
pp. 3135-3138 ◽  
Author(s):  
Lü Hong-Sheng ◽  
Zhang Hong-Bin ◽  
Gu Shu-Long
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
The Third

scholarly journals Linearizability of Nonlinear Third-Order Ordinary Differential Equations by Using a Generalized Linearizing Transformation

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
E. Thailert ◽  
S. Suksern
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Linear Equation ◽  
Ordinary Differential Equations ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
The Third ◽  
Linearization Problem ◽  
Linearizable Equation

We discuss the linearization problem of third-order ordinary differential equation under the generalized linearizing transformation. We identify the form of the linearizable equations and the conditions which allow the third-order ordinary differential equation to be transformed into the simplest linear equation. We also illustrate how to construct the generalized linearizing transformation. Some examples of linearizable equation are provided to demonstrate our procedure.

Construction of Green’s functional for a third order ordinary differential equation with general nonlocal conditions and variable principal coefficient

2020 ◽  
Vol 27 (4) ◽  
pp. 593-603 ◽  
Author(s):  
Kemal Özen
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Nonlocal Problem ◽  
Nonlocal Conditions ◽  
Adjoint Problem ◽  
Linear Ordinary Differential Equation ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Order Linear ◽  
Theoretical Results

AbstractIn this work, the solvability of a generally nonlocal problem is investigated for a third order linear ordinary differential equation with variable principal coefficient. A novel adjoint problem and Green’s functional are constructed for a completely nonhomogeneous problem. Several illustrative applications for the theoretical results are provided.

scholarly journals Existence Theory for Nonlinear Third-Order Ordinary Differential Equations with Nonlocal Multi-Point and Multi-Strip Boundary Conditions

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 281 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Mona Alsulami ◽  
Hari Srivastava ◽  
Bashir Ahmad ◽  
Sotiris Ntouyas
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Existence Theory ◽  
Ulam Stability ◽  
Point Boundary ◽  
Arbitrary Domain ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
The Third ◽  
Nonlocal Nonlinear

We investigate the solvability and Ulam stability for a nonlocal nonlinear third-order integro-multi-point boundary value problem on an arbitrary domain. The nonlinearity in the third-order ordinary differential equation involves the unknown function together with its first- and second-order derivatives. Our main results rely on the modern tools of functional analysis and are well illustrated with the aid of examples. An analogue problem involving non-separated integro-multi-point boundary conditions is also discussed.

scholarly journals A Functionally-Fitted Block Numerov Method for Solving Second-Order Initial-Value Problems with Oscillatory Solutions

2021 ◽  
Vol 18 (6) ◽  
Author(s):  
R. I. Abdulganiy ◽  
Higinio Ramos ◽  
O. A. Akinfenwa ◽  
S. A. Okunuga
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Initial Value Problems ◽  
Second Order ◽  
Initial Value ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Oscillatory Solutions ◽  
Type Method ◽  
Convergent Method

AbstractA functionally-fitted Numerov-type method is developed for the numerical solution of second-order initial-value problems with oscillatory solutions. The basis functions are considered among trigonometric and hyperbolic ones. The characteristics of the method are studied, particularly, it is shown that it has a third order of convergence for the general second-order ordinary differential equation, $$y''=f \left( x,y,y' \right) $$ y ′ ′ = f x , y , y ′ , it is a fourth order convergent method for the special second-order ordinary differential equation, $$y''=f \left( x,y\right) $$ y ′ ′ = f x , y . Comparison with other methods in the literature, even of higher order, shows the good performance of the proposed method.

scholarly journals Conservation laws for a Boussinesq equation.

2017 ◽  
Vol 2 (2) ◽  
pp. 465-472 ◽  
Author(s):  
M.L. Gandarias ◽  
M.S. Bruzón
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Conservation Laws ◽  
Boussinesq Equation ◽  
Point Of View ◽  
Multiplier Method ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Generalized Boussinesq Equation ◽  
The Relationship

AbstractIn this work, we study a generalized Boussinesq equation from the point of view of the Lie theory. We determine all the low-order conservation laws by using the multiplier method. Taking into account the relationship between symmetries and conservation laws and applying the multiplier method to a reduced ordinary differential equation, we obtain directly a second order ordinary differential equation and two third order ordinary differential equations.

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