Collocation approximations for weakly singular Volterra integro‐differential equations
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 convergenceHow to Cite
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Copyright (c) 2003 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2003 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.