Legendre-Galerkin spectral algorithm for fractional-order BVPs: Application to the Bagley-Torvik equation
S. M. Sayed, Admi Mohamed, Emad M. Abo-Eldahab, Y. H. Youssri
Abstract
<p>Herein, we provide an efficient spectral Galerkin algorithm, according to a special type of shifted Legendre basis for finding a semi-analytic solution to the Liouville-Caputo fractional boundary value problem. The algorithm’s main goal is to transform the fractional differential problem into a linear system with efficiently invertible, well-structured matrices. The convergence rates of the algorithm are carefully obtained as well as the error bound.</p>
Topics & Concepts
Legendre polynomialsMathematicsGalerkin methodInvertible matrixBoundary value problemConvergence (economics)Applied mathematicsFractional calculusOrder (exchange)Spectral methodMathematical analysisAlgorithmFinite element methodPure mathematicsFinancePhysicsThermodynamicsEconomic growthEconomicsFractional Differential Equations SolutionsDifferential Equations and Numerical MethodsNumerical methods for differential equations