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

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.

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