Geometric meshes and their application to Volterra integro-differential equations with singularities. (English) Zbl 0907.65142

Hu, Qiya

IMA J. Numer. Anal. 18, No. 1, 151-164 (1998).

The author studies Volterra integro-differential equations with weakly singular kernels. A new kind of mesh, the “geometric mesh”, is introduced. Then the corresponding \(\beta\)-polynomial collocation is discussed and it is shown that superconvergence properties may be obtained by using appropriate collocation parameters and such meshes. The main advantage of this technique is that one can greatly decrease the cost of computing. Numerical examples are treated.

Reviewer: Y.Cherruault (Paris)

MSC:

65R20	Numerical methods for integral equations
45J05	Integro-ordinary differential equations
45G05	Singular nonlinear integral equations

Keywords:

spline collocation methods; geometric mesh; numerical examples; Volterra integro-differential equations; weakly singular kernels; superconvergence