A New Legendre Spectral Galerkin and Pseudo-Spectral Approximations for Fractional Initial Value Problems

• Published in: Abstract and Applied Analysis Vol. 2013; no. 2013; pp. 237 - 246-322
• Main Authors: Bhrawy, Ali H., Alghamdi, Mohammad Ali
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Limiteds 01.01.2013; Hindawi Puplishing Corporation; Hindawi Publishing Corporation; John Wiley & Sons, Inc; Wiley
• Subjects: Algorithms; Approximation; Approximation theory; Boundary value problems; Differential equations; Functions (mathematics); Galerkin methods; Initial conditions; Mathematical analysis; Mathematical research; Numerical analysis; Polynomials; Spectra; Qatar

We extend the application of the Galerkin method for treating the multiterm fractional differential equations (FDEs) subject to initial conditions. A new shifted Legendre-Galerkin basis is constructed which satisfies exactly the homogeneous initial conditions by expanding the unknown variable using...