Soots, Hanna Britt; Lätt, Kaido; Pedas, Arvet Collocation based approximations for a class of fractional boundary value problems. (English) Zbl 1514.65204 Math. Model. Anal. 28, No. 2, 218-236 (2023). MSC: 65R20 34K37 45J05 PDFBibTeX XMLCite \textit{H. B. Soots} et al., Math. Model. Anal. 28, No. 2, 218--236 (2023; Zbl 1514.65204) Full Text: DOI
Lillemäe, Margus; Pedas, Arvet; Vikerpuur, Mikk Central part interpolation schemes for a class of fractional initial value problems. (English) Zbl 1491.65173 Acta Comment. Univ. Tartu. Math. 26, No. 1, 161-178 (2022). MSC: 65R20 34A08 45J05 45E10 65L05 65L60 PDFBibTeX XMLCite \textit{M. Lillemäe} et al., Acta Comment. Univ. Tartu. Math. 26, No. 1, 161--178 (2022; Zbl 1491.65173) Full Text: DOI
Diogo, Teresa; Pedas, Arvet; Vainikko, Gennadi Integral equations of the third kind in \(L^p\) spaces. (English) Zbl 1465.45001 J. Integral Equations Appl. 32, No. 4, 417-427 (2020). MSC: 45A05 45E10 PDFBibTeX XMLCite \textit{T. Diogo} et al., J. Integral Equations Appl. 32, No. 4, 417--427 (2020; Zbl 1465.45001) Full Text: DOI Euclid
Pedas, Arvet; Tamme, Enn; Vikerpuur, Mikk Numerical solution of linear fractional weakly singular integro-differential equations with integral boundary conditions. (English) Zbl 1437.65245 Appl. Numer. Math. 149, 124-140 (2020). MSC: 65R20 65L05 65L60 26A33 PDFBibTeX XMLCite \textit{A. Pedas} et al., Appl. Numer. Math. 149, 124--140 (2020; Zbl 1437.65245) Full Text: DOI
Pedas, Arvet; Tamme, Enn; Vikerpuur, Mikk Smoothing transformation and spline collocation for nonlinear fractional initial and boundary value problems. (English) Zbl 1357.65105 J. Comput. Appl. Math. 317, 1-16 (2017). MSC: 65L60 34A08 34A34 34B15 65L20 PDFBibTeX XMLCite \textit{A. Pedas} et al., J. Comput. Appl. Math. 317, 1--16 (2017; Zbl 1357.65105) Full Text: DOI
Diogo, T.; Lima, P. M.; Pedas, A.; Vainikko, G. Smoothing transformation and spline collocation for weakly singular Volterra integro-differential equations. (English) Zbl 1357.65316 Appl. Numer. Math. 114, 63-76 (2017). MSC: 65R20 45J05 45D05 45A05 45E10 PDFBibTeX XMLCite \textit{T. Diogo} et al., Appl. Numer. Math. 114, 63--76 (2017; Zbl 1357.65316) Full Text: DOI
Kolk, Marek; Pedas, Arvet; Tamme, Enn Smoothing transformation and spline collocation for linear fractional boundary value problems. (English) Zbl 1410.65284 Appl. Math. Comput. 283, 234-250 (2016). MSC: 65L60 34A08 65L20 PDFBibTeX XMLCite \textit{M. Kolk} et al., Appl. Math. Comput. 283, 234--250 (2016; Zbl 1410.65284) Full Text: DOI
Pedas, Arvet; Tamme, Enn; Vikerpuur, Mikk Spline collocation for fractional weakly singular integro-differential equations. (English) Zbl 1351.65103 Appl. Numer. Math. 110, 204-214 (2016). MSC: 65R20 45J05 26A33 PDFBibTeX XMLCite \textit{A. Pedas} et al., Appl. Numer. Math. 110, 204--214 (2016; Zbl 1351.65103) Full Text: DOI
Pedas, A.; Tamme, E.; Vikerpuur, M. Piecewise polynomial collocation for a class of fractional integro-differential equations. (English) Zbl 1336.65205 Constanda, Christian (ed.) et al., Integral methods in science and engineering. Theoretical and computational advances. Papers based on the presentations at the international conference, IMSE, Karlsruhe, Germany, July 21–25, 2014. Cham: Birkhäuser/Springer (ISBN 978-3-319-16726-8/hbk; 978-3-319-16727-5/ebook). 471-482 (2015). MSC: 65R20 45A05 45J05 26A33 PDFBibTeX XMLCite \textit{A. Pedas} et al., in: Integral methods in science and engineering. Theoretical and computational advances. Papers based on the presentations at the international conference, IMSE, Karlsruhe, Germany, July 21--25, 2014. Cham: Birkhäuser/Springer. 471--482 (2015; Zbl 1336.65205) Full Text: DOI
Pedas, Arvet; Tamme, Enn; Vikerpuur, Mikk Spline collocation for fractional integro-differential equations. (English) Zbl 1359.65310 Dimov, Ivan (ed.) et al., Finite difference methods, theory and applications. 6th international conference, FDM 2014, Lozenetz, Bulgaria, June 18–23, 2014. Revised selected papers. Cham: Springer (ISBN 978-3-319-20238-9/pbk; 978-3-319-20239-6/ebook). Lecture Notes in Computer Science 9045, 315-322 (2015). MSC: 65R20 45D05 45A05 26A33 PDFBibTeX XMLCite \textit{A. Pedas} et al., Lect. Notes Comput. Sci. 9045, 315--322 (2015; Zbl 1359.65310) Full Text: DOI
Kolk, Marek; Pedas, Arvet; Tamme, Enn Modified spline collocation for linear fractional differential equations. (English) Zbl 1311.65094 J. Comput. Appl. Math. 283, 28-40 (2015). MSC: 65L05 65L60 34A30 34A08 65R20 45D05 65L20 65L70 PDFBibTeX XMLCite \textit{M. Kolk} et al., J. Comput. Appl. Math. 283, 28--40 (2015; Zbl 1311.65094) Full Text: DOI
Pedas, Arvet; Tamme, Enn Spline collocation for nonlinear fractional boundary value problems. (English) Zbl 1337.65106 Appl. Math. Comput. 244, 502-513 (2014). MSC: 65L60 34A08 PDFBibTeX XMLCite \textit{A. Pedas} and \textit{E. Tamme}, Appl. Math. Comput. 244, 502--513 (2014; Zbl 1337.65106) Full Text: DOI
Pedas, Arvet; Tamme, Enn Numerical solution of nonlinear fractional differential equations by spline collocation methods. (English) Zbl 1291.65247 J. Comput. Appl. Math. 255, 216-230 (2014). MSC: 65L60 65L05 26A33 PDFBibTeX XMLCite \textit{A. Pedas} and \textit{E. Tamme}, J. Comput. Appl. Math. 255, 216--230 (2014; Zbl 1291.65247) Full Text: DOI
Kolk, Marek; Pedas, Arvet Numerical solution of Volterra integral equations with singularities. (English) Zbl 1273.65197 Front. Math. China 8, No. 2, 239-259 (2013). MSC: 65R20 45D05 PDFBibTeX XMLCite \textit{M. Kolk} and \textit{A. Pedas}, Front. Math. China 8, No. 2, 239--259 (2013; Zbl 1273.65197) Full Text: DOI
Pedas, Arvet; Tamme, Enn Piecewise polynomial collocation for linear boundary value problems of fractional differential equations. (English) Zbl 1245.65104 J. Comput. Appl. Math. 236, No. 13, 3349-3359 (2012). Reviewer: Kevin Burrage (Brisbane) MSC: 65L60 PDFBibTeX XMLCite \textit{A. Pedas} and \textit{E. Tamme}, J. Comput. Appl. Math. 236, No. 13, 3349--3359 (2012; Zbl 1245.65104) Full Text: DOI
Pedas, Arvet; Tamme, Enn Spline collocation methods for linear multi-term fractional differential equations. (English) Zbl 1229.65138 J. Comput. Appl. Math. 236, No. 2, 167-176 (2011). Reviewer: Kai Diethelm (Braunschweig) MSC: 65L60 65L05 65R20 34A08 34A30 65L20 65L70 PDFBibTeX XMLCite \textit{A. Pedas} and \textit{E. Tamme}, J. Comput. Appl. Math. 236, No. 2, 167--176 (2011; Zbl 1229.65138) Full Text: DOI
Pedas, Arvet; Tamme, Enn On the convergence of spline collocation methods for solving fractional differential equations. (English) Zbl 1217.65154 J. Comput. Appl. Math. 235, No. 12, 3502-3514 (2011). Reviewer: Vicenţiu D. Rădulescu (Craiova) MSC: 65L20 65L60 34A08 65L50 65L10 PDFBibTeX XMLCite \textit{A. Pedas} and \textit{E. Tamme}, J. Comput. Appl. Math. 235, No. 12, 3502--3514 (2011; Zbl 1217.65154) Full Text: DOI
Pedas, Arvet; Tamme, Enn A discrete collocation method for Fredholm integro-differential equations with weakly singular kernels. (English) Zbl 1216.65186 Appl. Numer. Math. 61, No. 6, 738-751 (2011). Reviewer: Kai Diethelm (Braunschweig) MSC: 65R20 45A05 45J05 PDFBibTeX XMLCite \textit{A. Pedas} and \textit{E. Tamme}, Appl. Numer. Math. 61, No. 6, 738--751 (2011; Zbl 1216.65186) Full Text: DOI
Orav-Puurand, Kerli; Pedas, Arvet; Vainikko, Gennadi Nyström type methods for Fredholm integral equations with weak singularities. (English) Zbl 1193.65226 J. Comput. Appl. Math. 234, No. 9, 2848-2858 (2010). Reviewer: I. V. Boikov (Penza) MSC: 65R20 45B05 45E10 PDFBibTeX XMLCite \textit{K. Orav-Puurand} et al., J. Comput. Appl. Math. 234, No. 9, 2848--2858 (2010; Zbl 1193.65226) Full Text: DOI
Pallav, Rene; Pedas, Arvet Quadratic spline collocation for the smoothed weakly singular Fredholm integral equations. (English) Zbl 1187.65150 Numer. Funct. Anal. Optim. 30, No. 9-10, 1048-1064 (2009). Reviewer: I. V. Boikov (Penza) MSC: 65R20 45B05 45E10 PDFBibTeX XMLCite \textit{R. Pallav} and \textit{A. Pedas}, Numer. Funct. Anal. Optim. 30, No. 9--10, 1048--1064 (2009; Zbl 1187.65150) Full Text: DOI
Kolk, Marek; Pedas, Arvet; Vainikko, Gennadi High-order methods for Volterra integral equations with general weak singularities. (English) Zbl 1187.65145 Numer. Funct. Anal. Optim. 30, No. 9-10, 1002-1024 (2009). Reviewer: I. V. Boikov (Penza) MSC: 65R20 45D05 45E10 45A05 PDFBibTeX XMLCite \textit{M. Kolk} et al., Numer. Funct. Anal. Optim. 30, No. 9--10, 1002--1024 (2009; Zbl 1187.65145) Full Text: DOI
Pedas, Arvet; Vainikko, Gennadi On the regularity of solutions to integral equations with nonsmooth kernels on a union of open intervals. (English) Zbl 1168.45003 J. Comput. Appl. Math. 229, No. 2, 440-451 (2009). Reviewer: Adrian Carabineanu (Bucureşti) MSC: 45E10 45M05 PDFBibTeX XMLCite \textit{A. Pedas} and \textit{G. Vainikko}, J. Comput. Appl. Math. 229, No. 2, 440--451 (2009; Zbl 1168.45003) Full Text: DOI
Pedas, Arvet; Tamme, Enn Discrete Galerkin method for Fredholm integro-differential equations with weakly singular kernels. (English) Zbl 1137.65073 J. Comput. Appl. Math. 213, No. 1, 111-126 (2008). Reviewer: Lechoslaw Hącia (Poznań) MSC: 65R20 45J05 45E10 PDFBibTeX XMLCite \textit{A. Pedas} and \textit{E. Tamme}, J. Comput. Appl. Math. 213, No. 1, 111--126 (2008; Zbl 1137.65073) Full Text: DOI
Pedas, Arvet; Vainikko, Gennadi Integral equations with diagonal and boundary singularities of the kernel. (English) Zbl 1118.45003 Z. Anal. Anwend. 25, No. 4, 487-516 (2006). Reviewer: Roland Duduchava (Tbilisi) MSC: 45E10 45M05 PDFBibTeX XMLCite \textit{A. Pedas} and \textit{G. Vainikko}, Z. Anal. Anwend. 25, No. 4, 487--516 (2006; Zbl 1118.45003) Full Text: DOI
Pedas, Arvet; Tamme, Enn Spline collocation method for integro-differential equations with weakly singular kernels. (English) Zbl 1104.65129 J. Comput. Appl. Math. 197, No. 1, 253-269 (2006). Reviewer: Kai Diethelm (Braunschweig) MSC: 65R20 45J05 45E10 PDFBibTeX XMLCite \textit{A. Pedas} and \textit{E. Tamme}, J. Comput. Appl. Math. 197, No. 1, 253--269 (2006; Zbl 1104.65129) Full Text: DOI
Brunner, Hermann; Pedas, Arvet; Vainikko, Gennadi The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations. (English) Zbl 0941.65136 Math. Comput. 68, No. 227, 1079-1095 (1999). Reviewer: J.Elschner (Berlin) MSC: 65R20 45G05 PDFBibTeX XMLCite \textit{H. Brunner} et al., Math. Comput. 68, No. 227, 1079--1095 (1999; Zbl 0941.65136) Full Text: DOI
Pedas, Arvet; Vainikko, Gennadi Superconvergence of piecewise polynomial collocations for nonlinear weakly singular integral equations. (English) Zbl 0910.65115 J. Integral Equations Appl. 9, No. 4, 379-406 (1997). Reviewer: H.Brunner (St.John’s) MSC: 65R20 45G05 PDFBibTeX XMLCite \textit{A. Pedas} and \textit{G. Vainikko}, J. Integral Equations Appl. 9, No. 4, 379--406 (1997; Zbl 0910.65115) Full Text: DOI Link