Spline Collocation for Multi-Term Fractional Integro-Differential Equations with Weakly Singular Kernels
Arvet Pedas, Mikk Vikerpuur
Abstract
We consider general linear multi-term Caputo fractional integro-differential equations with weakly singular kernels subject to local or non-local boundary conditions. Using an integral equation reformulation of the proposed problem, we first study the existence, uniqueness and regularity of the exact solution. Based on the obtained regularity properties and spline collocation techniques, the numerical solution of the problem is discussed. Optimal global convergence estimates are derived and a superconvergence result for a special choice of grid and collocation parameters is given. A numerical illustration is also presented.
Topics & Concepts
MathematicsSuperconvergenceCollocation methodUniquenessCollocation (remote sensing)Term (time)Mathematical analysisSpline (mechanical)Applied mathematicsBoundary value problemConvergence (economics)Differential equationOrdinary differential equationFinite element methodComputer scienceStructural engineeringQuantum mechanicsEngineeringThermodynamicsMachine learningPhysicsEconomic growthEconomicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods