scholarly journals New Properties of Modified Second Kind Chebyshev Polynomials

2020 ◽  
Vol 55 (3) ◽  
Author(s):  
Semaa Hassan Aziz ◽  
Mohammed Rasheed ◽  
Suha Shihab
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Chebyshev Polynomial ◽  
Chebyshev Polynomials ◽  
Digital Computer ◽  
Higher Order ◽  
Algebraic Equations ◽  
Equation Problem ◽  
Higher Order Differential Equations

Modified second kind Chebyshev polynomials for solving higher order differential equations are presented in this paper. This technique, along with some new properties of such polynomials, will reduce the original differential equation problem to the solution of algebraic equations with a straightforward and computational digital computer. Some illustrative examples are included. The modified second kind Chebyshev polynomial is calculated using only a small number of the modified second kind Chebyshev polynomials, which leads to attractive results.

On the eigenvectors for a class of matrices arising from quasi-derivatives

1984 ◽  
Vol 97 ◽  
pp. 73-78 ◽  
Author(s):  
M. S. P. Eastham
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Asymptotic Theory ◽  
Higher Order ◽  
Symmetric Matrices ◽  
Convenient Formula ◽  
Class Of Matrices ◽  
Higher Order Differential Equations

SynopsisLet A be a product of symmetric matrices, A = RQ, with R non-singular, and let v be an eigenvector of A. For certain R and Q, a convenient formula for the expression (R−1v)tv is obtained. This expression occurs in the diagonalization of A and, in the particular case where A is associated with the quasi-derivative formulation of higher-order differential equations, the expression occurs in the asymptotic theory of solutions of the differential equation.

scholarly journals Twin positive solutions for three-point boundary value problems of higher-order differential equations

2004 ◽  
Vol 2004 (39) ◽  
pp. 2049-2063
Author(s):  
Yuji Liu ◽  
Weigao Ge
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Higher Order ◽  
Point Boundary ◽  
Higher Order Differential Equations

A new fixed point theorem on cones is applied to obtain the existence of at least two positive solutions of a higher-order three-point boundary value problem for the differential equation subject to a class ofboundary value conditions. The associated Green's function is given. Some results obtained recently are generalized.

scholarly journals Probabilistic Representations for the Solution of Higher Order Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
S. Mazzucchi
Keyword(s):  
Differential Equation ◽  
Stochastic Process ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Higher Order ◽  
Probabilistic Representation ◽  
Partial Differential ◽  
Complex Valued ◽  
Higher Order Differential Equations

A probabilistic representation for the solution of the partial differential equation (∂/∂t)u(t,x)=−αΔ2u(t,x),α∈ℂ, is constructed in terms of the expectation with respect to the measure associated to a complex-valued stochastic process.

scholarly journals Oscillation Results for Nonlinear Higher-Order Differential Equations with Delay Term

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 446
Author(s):  
Alanoud Almutairi ◽  
Omar Bazighifan ◽  
Youssef N. Raffoul
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Higher Order ◽  
Middle Term ◽  
Delay Term ◽  
Integral Averaging Technique ◽  
Equations With Delay ◽  
Oscillation Of Solutions ◽  
Comparison Technique ◽  
Higher Order Differential Equations

The aim of this work is to investigate the oscillation of solutions of higher-order nonlinear differential equations with a middle term. By using the integral averaging technique, Riccati transformation technique and comparison technique, several oscillatory properties are presented that unify the results obtained in the literature. Some examples are presented to demonstrate the main results.

scholarly journals Asymptotic Dichotomy in a Class of Third-Order Nonlinear Differential Equations with Impulses

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Kun-Wen Wen ◽  
Gen-Qiang Wang ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Functional Differential Equations ◽  
Higher Order ◽  
Third Order ◽  
Order Nonlinear Differential Equation ◽  
Functional Differential

Solutions of quite a few higher-order delay functional differential equations oscillate or converge to zero. In this paper, we obtain several such dichotomous criteria for a class of third-order nonlinear differential equation with impulses.

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