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A Legendre Computational Matrix Method for Solving High-Order Fractional Differential Equations |
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| รหัสดีโอไอ | |
| Creator | Mohamed Meabed KHADER, Ahmed Saied HENDY |
| Title | A Legendre Computational Matrix Method for Solving High-Order Fractional Differential Equations |
| Publisher | Walailak University |
| Publication Year | 2557 |
| Journal Title | Walailak Journal of Science and Technology |
| Journal Vol. | 11 |
| Journal No. | 4 |
| Page no. | 289-305 |
| Keyword | Ordinary fractional differential equations, shifted Legendre polynomials, Caputo derivatives, computational matrix method, cauchy equations, Bagley-Torvik equations |
| ISSN | 1686-3933 |
| Abstract | In this paper, a matrix method for the approximate solution of high order fractional differential equations (FDEs) in terms of a truncated Legendre series is presented. The FDEs and its initial or boundary conditions are transformed to matrix equations, which correspond to a system of algebraic equations with unknown Legendre coefficients. The solution of this system yields the Legendre coefficients of the solution formula. Several numerical examples, such as Cauchy and Bagley-Torvik fractional differential equations, are provided to confirm the accuracy and the effectiveness of the proposed method. |
