High‐order ADI orthogonal spline collocation method for a new 2D fractional integro‐differential problem
Leijie Qiao, Da Xu, Yubin Yan
Abstract
We use the generalized L1 approximation for the Caputo fractional derivative, the second‐order fractional quadrature rule approximation for the integral term, and a classical Crank‐Nicolson alternating direction implicit (ADI) scheme for the time discretization of a new two‐dimensional (2D) fractional integro‐differential equation, in combination with a space discretization by an arbitrary‐order orthogonal spline collocation (OSC) method. The stability of a Crank‐Nicolson ADI OSC scheme is rigourously established, and error estimate is also derived. Finally, some numerical tests are given.
Topics & Concepts
MathematicsDiscretizationQuadrature (astronomy)Crank–Nicolson methodCollocation (remote sensing)Spline (mechanical)Alternating direction implicit methodFractional calculusOrthogonal collocationMathematical analysisIntegro-differential equationApplied mathematicsGaussian quadratureCollocation methodDifferential equationNyström methodFinite difference methodIntegral equationOrdinary differential equationRiccati equationElectrical engineeringGeologyRemote sensingStructural engineeringEngineeringFractional Differential Equations SolutionsDifferential Equations and Numerical MethodsNumerical methods for differential equations