A UNIQUENESS THEOREM IN THE INVERSE SPECTRAL THEORY OF A CERTAIN HIGHER-ORDER ORDINARY DIFFERENTIAL EQUATION USING PALEY–WIENER METHODS

2005 ◽  
Vol 72 (01) ◽  
pp. 169-184
Author(s):  
E. ANDERSSON
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Uniqueness Theorem ◽  
Spectral Theory ◽  
Higher Order ◽  
Order Ordinary Differential Equation ◽  
Inverse Spectral Theory ◽  
Inverse Spectral

scholarly journals New Modified Adomin Decomp osition Metho d for Boundary Value Problems of Higher-order Ordinary Differential Equation

2020 ◽  
pp. 20-37
Author(s):  
Zainab Ali Ab du Al-Rabahi ◽  
Yahya Qaid Hasan
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Operator ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Inverse Operator ◽  
Higher Order ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Solving Equations

This study will present a new modified differential operator for solving third-order boundary value problems into higher-order ordinary differential equation. We found the differential operator for new three inverse operator which can be applied for solving equations at more than one type in different conditions. We put a detailed plan for five non-linear examples from a high-order, we get dynamic and quickly to the exact solution.

scholarly journals WKB periods for higher order ODE and TBA equations

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Katsushi Ito ◽  
Takayasu Kondo ◽  
Kohei Kuroda ◽  
Hongfei Shu
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Field Equation ◽  
Lie Algebra ◽  
Bethe Ansatz ◽  
Linear Problem ◽  
Higher Order ◽  
Quantum Corrections ◽  
Order Ordinary Differential Equation ◽  
Quadratic Potential

Abstract We study the WKB periods for the (r + 1)-th order ordinary differential equation (ODE) which is obtained by the conformal limit of the linear problem associated with the $$ {A}_r^{(1)} $$ A r 1 affine Toda field equation. We compute the quantum corrections by using the Picard-Fuchs operators. The ODE/IM correspondence provides a relation between the Wronskians of the solutions and the Y-functions which satisfy the thermodynamic Bethe ansatz (TBA) equation related to the Lie algebra Ar. For the quadratic potential, we propose a formula to show the equivalence between the logarithm of the Y-function and the WKB period, which is confirmed by solving the TBA equation numerically.

scholarly journals The System of Differential Equations Associated With Involutions

2021 ◽  
Author(s):  
Farrukh Nuriddin ugli Dekhkonov
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Initial Value Problem ◽  
Initial Conditions ◽  
Higher Order ◽  
System Of Differential Equations ◽  
Initial Value ◽  
Order Ordinary Differential Equation

In this paper, we consider with a class of system of differential equations whose argument transforms are involution. In this an initial value problem for a differential equation with involution is reduced to an initial value problem for a higher order ordinary differential equation. Than either two initial conditions are necessary for a solution, the equation is then reduced to a boundary value problem for a higher order ODE.

Generalized plane stress in a semi-infinite strip under arbitrary end-load

1964 ◽  
Vol 281 (1385) ◽  
pp. 184-206 ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Plane Stress ◽  
Stress Function ◽  
Infinite Strip ◽  
Order Ordinary Differential Equation ◽  
Orthogonal Functions

The problem involves the determination of a biharmonic generalized plane-stress function satisfying certain boundary conditions. We expand the stress function in a series of non-orthogonal eigenfunctions. Each of these is expanded in a series of orthogonal functions which satisfy a certain fourth-order ordinary differential equation and the boundary conditions implied by the fact that the sides are stress-free. By this method the coefficients involved in the biharmonic stress function corresponding to any arbitrary combination of stress on the end can be obtained directly from two numerical matrices published here The method is illustrated by four examples which cast light on the application of St Venant’s principle to the strip. In a further paper by one of the authors, the method will be applied to the problem of the finite rectangle.

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