A highly accurate Jacobi collocation algorithm for systems of high-order linear differential-difference equations with mixed initial conditions

2015 ◽  
Vol 38 (14) ◽  
pp. 3022-3032 ◽  
Author(s):  
A. H. Bhrawy ◽  
E. H. Doha ◽  
D. Baleanu ◽  
R. M. Hafez
Keyword(s):  
Difference Equations ◽  
Initial Conditions ◽  
High Order ◽  
Order Linear ◽  
Linear Differential

Numerical Solutions of Systems of High-Order Linear Differential-Difference Equations with Bessel Polynomial Bases

2011 ◽  
Vol 66 (8-9) ◽  
pp. 519-532 ◽  
Author(s):  
Șuayip Yüzbași ◽  
Niyazi Șahin ◽  
Ahmet Yıldırımb
Keyword(s):  
Difference Equations ◽  
Numerical Solutions ◽  
Variable Coefficients ◽  
High Order ◽  
Numerical Examples ◽  
Order Linear ◽  
Collocation Points ◽  
Bessel Polynomial ◽  
Polynomial Bases ◽  
Linear Differential

Abstract In this paper, a numerical matrix method, which is based on collocation points, is presented for the approximate solution of a system of high-order linear differential-difference equations with variable coefficients under the mixed conditions in terms of Bessel polynomials. Numerical examples are included to demonstrate the validity and applicability of the technique and comparisons are made with existing results. The results show the efficiency and accuracy of the present work. All of the numerical computations have been performed on computer using a program written in MATLAB v7.6.0 (R2008a).

scholarly journals Solving Second-Order Linear Differential Equations with Random Analytic Coefficients about Regular-Singular Points

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 230
Author(s):  
Juan-Carlos Cortés ◽  
Ana Navarro-Quiles ◽  
José-Vicente Romero ◽  
María-Dolores Roselló
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Random Variable ◽  
Second Order ◽  
Singular Points ◽  
Linear Differential Equations ◽  
Transformation Technique ◽  
Order Linear ◽  
Bessel Differential Equation ◽  
Linear Differential

In this contribution, we construct approximations for the density associated with the solution of second-order linear differential equations whose coefficients are analytic stochastic processes about regular-singular points. Our analysis is based on the combination of a random Fröbenius technique together with the random variable transformation technique assuming mild probabilistic conditions on the initial conditions and coefficients. The new results complete the ones recently established by the authors for the same class of stochastic differential equations, but about regular points. In this way, this new contribution allows us to study, for example, the important randomized Bessel differential equation.

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