Spline Collocation for Fractional Integro-Differential Equations
We consider a class of boundary value problems for fractional integro-differential equations. Using an integral equation reformulation of the boundary value problem, we first study the regularity of the exact solution. Based on the obtained regularity properties and spline collocation techniques, the numerical solution of the boundary value problem by suitable non-polynomial approximations is discussed. Optimal global convergence estimates are derived and a super-convergence result for a special choice of grid and collocation parameters is given. A numerical illustration is also presented.
This work was supported by Estonian Science Foundation Grant No. 9104 and Estonian Institutional Research Project IUT 20-57.