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 Initiation of thermal explosion by intense light: criticality dependence on data and parameters

1987 ◽  
Vol 28 (3) ◽  
pp. 287-295 ◽  
Author(s):  
K. K. Tam
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Steady State Solution ◽  
Linear Ordinary Differential Equation ◽  
Critical Parameters ◽  
Linear Parabolic Equation ◽  
Thermal Ignition ◽  
Non Linear ◽  
Intense Light

AbstractA model for thermal ignition by intense light is studied. The governing non-linear parabolic equation is linearized in a two-step manner with the aid of a non-linear ordinary differential equation which captures the salient features of the non-linear parabolic equation. The critical parameters are computed from the steady-state solution of the ordinary differential equation, which can be obtained without actually solving the equation. Comparison with available data shows that the present method yields good results.

scholarly journals A REPRESENTATIVE SOLUTION TO M-ORDER LINEAR ORDINARY DIFFERENTIAL EQUATION WITH NONLOCAL CONDITIONS BY GREEN'S FUNCTIONAL CONCEPT

2012 ◽  
Vol 17 (4) ◽  
pp. 571-588 ◽  
Author(s):  
Kemal Ozen ◽  
Kamil Orucoglu
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Nonlocal Conditions ◽  
Adjoint System ◽  
Linear Ordinary Differential Equation ◽  
The Other ◽  
Algebraic Equations ◽  
Order Ordinary Differential Equation ◽  
Multipoint Problem ◽  
Nonsmooth Coefficients

In this work, we investigate a linear completely nonhomogeneous nonlocal multipoint problem for an m-order ordinary differential equation with generally variable nonsmooth coefficients satisfying some general properties such as p-integrability and boundedness. A system of m + 1 integro-algebraic equations called the special adjoint system is constructed for this problem. Green's functional is a solution of this special adjoint system. Its first component corresponds to Green's function for the problem. The other components correspond to the unit effects of the conditions. A solution to the problem is an integral representation which is based on using this new Green's functional. Some illustrative implementations and comparisons are provided with some known results in order to demonstrate the advantages of the proposed approach.

scholarly journals General Solution Of Nth-Order Linear Ordinary Differential Equation

2021 ◽  
Author(s):  
Rajnish Kumar Jha
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
General Solution ◽  
Linear Ordinary Differential Equation ◽  
Order Linear ◽  
Special Case ◽  
Integrating Factors

In this paper we present a solution expression for the general Nth-order linear ordinary differential equation as our main result which involves the use of Integrating Factors where the Integrating Factors are determined using a set of equations such that when this set of equations can be solved, the solution of the concerned differential equation can be determined completely. In this regard we also present result for a special case corresponding to the main result where the solution of the general Nth-order linear ordinary differential equation can be determined completely when N-1 out of N complementary solutions are known.

scholarly journals General Solution Of Nth-Order Linear Ordinary Differential Equation With Constant Coefficients

2021 ◽  
Author(s):  
Rajnish Kumar Jha
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
General Solution ◽  
Linear Ordinary Differential Equation ◽  
Order Linear ◽  
Constant Coefficients

In this paper we present a formula for the general solution of Nth-order linear ordinary differential equation with constant coefficients as our main result. In this regard we also present two supporting results in this paper which reduce the order of the concerned differential equation by one and give the relation between the coefficients of the initial differential equation and the differential equation obtained. We also discuss about the complementary solution and homogeneous equations with regard to the main result described in this paper.

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