Chebyshev polynomial solutions of systems of high-order linear differential equations with variable coefficients

2003 ◽  
Vol 144 (2-3) ◽  
pp. 237-247 ◽  
Author(s):  
Ayşegül Akyüz ◽  
Mehmet Sezer
Keyword(s):  
Differential Equations ◽  
Chebyshev Polynomial ◽  
Variable Coefficients ◽  
High Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Polynomial Solutions ◽  
Linear Differential

scholarly journals Lucas Polynomial Approach for System of High-Order Linear Differential Equations and Residual Error Estimation

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Muhammed Çetin ◽  
Mehmet Sezer ◽  
Coşkun Güler
Keyword(s):  
Differential Equations ◽  
Approximate Solutions ◽  
Variable Coefficients ◽  
High Order ◽  
Linear Differential Equations ◽  
Algebraic Equations ◽  
Order Linear ◽  
Lucas Polynomials ◽  
Linear Algebraic Equations ◽  
Linear Differential

An approximation method based on Lucas polynomials is presented for the solution of the system of high-order linear differential equations with variable coefficients under the mixed conditions. This method transforms the system of ordinary differential equations (ODEs) to the linear algebraic equations system by expanding the approximate solutions in terms of the Lucas polynomials with unknown coefficients and by using the matrix operations and collocation points. In addition, the error analysis based on residual function is developed for present method. To demonstrate the efficiency and accuracy of the method, numerical examples are given with the help of computer programmes written inMapleandMatlab.

scholarly journals Hyers-Ulam Stability of the First-Order Matrix Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Soon-Mo Jung
Keyword(s):  
Differential Equations ◽  
Variable Coefficients ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Order Linear ◽  
First Order ◽  
Matrix Differential Equations ◽  
Homogeneous Matrix ◽  
Linear Differential ◽  
Matrix Differential

We prove the generalized Hyers-Ulam stability of the first-order linear homogeneous matrix differential equationsy→'(t)=A(t)y→(t). Moreover, we apply this result to prove the generalized Hyers-Ulam stability of thenth order linear differential equations with variable coefficients.

scholarly journals Distributions of Zeros of Solutions for Third-Order Differential Equations with Variable Coefficients

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Samir H. Saker ◽  
Mohammed A. Arahet
Keyword(s):  
Differential Equations ◽  
Lower Bounds ◽  
Variable Coefficients ◽  
Linear Differential Equations ◽  
Third Order ◽  
Order Linear ◽  
The Third ◽  
Hardy's Inequality ◽  
Zeros Of Solutions ◽  
Linear Differential

For the third-order linear differential equations of the formr(t)x′′(t)′+p(t)x′(t)+q(t)x(t)=0, we will establish lower bounds for the distance between zeros of a solution and/or its derivatives. The main results will be proved by making use of Hardy’s inequality and some generalizations of Opial and Wirtinger type inequalities.

scholarly journals APL and the numerical solution of high‐order linear differential equations

1983 ◽  
Vol 51 (8) ◽  
pp. 743-746
Author(s):  
Neil A. Gershenfeld ◽  
Edward H. Schadler ◽  
O. M. Bilaniuk
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
High Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Linear Differential
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