Applications of Fractional Differentiation Matrices in Solving Caputo Fractional Differential Equations
Zhongshu Wu, Xinxia Zhang, Jihan Wang, Xiaoyan Zeng
Abstract
This paper pursues obtaining Jacobi spectral collocation methods to solve Caputo fractional differential equations numerically. We used the shifted Jacobi–Gauss–Lobatto or Jacobi–Gauss–Radau quadrature nodes as the collocation points and derived the fractional differentiation matrices for Caputo fractional derivatives. With the fractional differentiation matrices, the fractional differential equations were transformed into linear systems, which are easier to solve. Two types of fractional differential equations were used for the numerical simulations, and the numerical results demonstrated the fast convergence and high accuracy of the proposed methods.
Topics & Concepts
MathematicsFractional calculusGaussCollocation methodQuadrature (astronomy)Orthogonal collocationCollocation (remote sensing)Convergence (economics)Applied mathematicsSpectral methodDifferential equationMathematical analysisGaussian quadratureNyström methodIntegral equationOrdinary differential equationComputer sciencePhysicsMachine learningQuantum mechanicsEconomicsOpticsEconomic growthFractional Differential Equations SolutionsDifferential Equations and Numerical MethodsIterative Methods for Nonlinear Equations