Collocation approximations for weakly singular Volterra integro‐differential equations¹

This work was supported by the Estonian Science Foundation (Grant No. 4410)

Abstract

A piecewise polynomial collocation method for solving linear weakly singular integro‐differential equations of Volterra type is constructed. The attainable order of convergence of collocation approximations on arbitrary and quasi‐uniform grids is studied theoretically and numerically.

Darbe nagrinejamas silpnai singuliariu Voltero integraliniu‐diferencialiniu lygčiu skaitinio artinio radimo algoritmas. Integralai priklauso ne tik nuo sprendinio, bet ir nuo jo pirmosios išvestines. Ištirtas kolokaciju metodo tikslumas, kai naudojami netolygūs ir artimi tolygiems tinklai. Teoriniai iverčiai patvirtinti skaičiavimo eksperimento rezultatais.

Key words:

• Weakly singular Volterra integro‐differential equation
• piecewise polynomial collocation method
• order of convergence

Notes

This work was supported by the Estonian Science Foundation (Grant No. 4410)