Collocation approximations for weakly singular Volterra integro‐differential equations

    I. Parts Info
    A. Pedas Info

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.

Silpnai singuliarių Voltero integralinių-diferencialinių lygčių aproksimavimas kolokacijų metodu

Santrauka. Darbe nagrinėjamas silpnai singuliarių Voltero integralinių‐diferencialinių lygčių skaitinio artinio radimo algoritmas. Integralai priklauso ne tik nuo sprendinio, bet ir nuo jo pirmosios išvestinės. Ištirtas kolokacijų metodo tikslumas, kai naudojami netolygūs ir artimi tolygiems tinklai. Teoriniai įverčiai patvirtinti skaičiavimo eksperimento rezultatais.

First Published Online: 14 Oct 2010

Keywords:

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

How to Cite

Parts, I., & Pedas, A. (2003). Collocation approximations for weakly singular Volterra integro‐differential equations. Mathematical Modelling and Analysis, 8(4), 315-328. https://doi.org/10.3846/13926292.2003.9637233

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December 31, 2003
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2003-12-31

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How to Cite

Parts, I., & Pedas, A. (2003). Collocation approximations for weakly singular Volterra integro‐differential equations. Mathematical Modelling and Analysis, 8(4), 315-328. https://doi.org/10.3846/13926292.2003.9637233

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