A novel operational matrix for the numerical solution of nonlinear Lane-Emden system of fractional order. (English) Zbl 1476.65133
Summary: In this work, we introduce a numerical method for solving nonlinear fractional system of Lane-Emden type equations. The proposed technique is based on Dickson operational matrix of a fractional derivative. First, we deduce the Dickson operational matrix of the fractional derivative using Dickson polynomial, and then, the obtained matrix is unitized to convert the fractional Lane-Emden system with its initial conditions into a system of nonlinear algebraic equations. This system of algebraic equations can be solved numerically via Newton’s iteration method. An error estimate of the proposed method is derived. Numerical examples are provided to demonstrate the validity, applicability, and accuracy of the new technique.
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 33C47 | Other special orthogonal polynomials and functions |
| 34A08 | Fractional ordinary differential equations |
| 34A45 | Theoretical approximation of solutions to ordinary differential equations |
| 65L70 | Error bounds for numerical methods for ordinary differential equations |
Keywords:
Dickson polynomials; Caputo differential operator; spectral collocation method; nonlinear system of Lane-Emden type in the fractional-order; operational matrixReferences:
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