Discrete spectral Tau shifted Chebyshev method for solving a system Volterra integro-fractional differential equations
Suha SHIHAB, Shazad Shawki Ahmed
Abstract
The work in this paper presents a novel explicit formula to define the derivative of shifted Chebyshev polynomials for any fractional orders in Caputo sense. An efficient direct spectral Tau technique is also developed in this work to find the approximate solution of the system of linear Volterra integro-fractional differential equations (LVIFDEs) using shifted Chebyshev polynomials T(a,b)m (t) for t ∈ (a,b ), b > 0 and m is the degree of shifted Chebyshev polynomial. Tau shifted Chebyshev method together with Chebyshev-Gauss-Lobatto collocation points are utilized as collocation nodes for numerically treading LVIFDEs. Three numerical examples are contained to illustrate the efficiency of the suggested.
Topics & Concepts
Chebyshev filterChebyshev polynomialsApplied mathematicsChebyshev equationDifferential equationVolterra equationsFractional calculusComputer scienceMathematical analysisMathematicsPhysicsOrthogonal polynomialsNonlinear systemClassical orthogonal polynomialsQuantum mechanicsFractional Differential Equations SolutionsDifferential Equations and Numerical MethodsIterative Methods for Nonlinear Equations