Chatziafratis, Andreas; Kamvissis, Spyridon; Stratis, Ioannis G. Boundary behavior of the solution to the linear Korteweg-de Vries equation on the half line. (English) Zbl 07801251 Stud. Appl. Math. 150, No. 2, 339-379 (2023). MSC: 35Q53 35A09 35C05 35B65 37K10 35Q15 PDFBibTeX XMLCite \textit{A. Chatziafratis} et al., Stud. Appl. Math. 150, No. 2, 339--379 (2023; Zbl 07801251) Full Text: DOI
Colbrook, Matthew J.; Ayton, Lorna J.; Fokas, Athanassios S. The unified transform for mixed boundary condition problems in unbounded domains. (English) Zbl 1472.74115 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 475, No. 2222, Article ID 20180605, 21 p. (2019); correction ibid. 475, No. 2224, Article ID 20190201, 1 p. (2019). MSC: 74J20 PDFBibTeX XMLCite \textit{M. J. Colbrook} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 475, No. 2222, Article ID 20180605, 21 p. (2019; Zbl 1472.74115) Full Text: DOI Link
Colbrook, Matthew J.; Fokas, Thanasis S.; Hashemzadeh, Parham A hybrid analytical-numerical technique for elliptic pdes. (English) Zbl 1414.65039 SIAM J. Sci. Comput. 41, No. 2, A1066-A1090 (2019). MSC: 65N35 65N12 35J25 PDFBibTeX XMLCite \textit{M. J. Colbrook} et al., SIAM J. Sci. Comput. 41, No. 2, A1066--A1090 (2019; Zbl 1414.65039) Full Text: DOI
Grylonakis, E.-N. G.; Filelis-Papadopoulos, C. K.; Gravvanis, G. A.; Fokas, A. S. An iterative spatial-stepping numerical method for linear elliptic PDEs using the unified transform. (English) Zbl 1506.65244 J. Comput. Appl. Math. 352, 194-209 (2019). MSC: 65N99 65N35 65N38 35C15 35J05 35J25 PDFBibTeX XMLCite \textit{E. N. G. Grylonakis} et al., J. Comput. Appl. Math. 352, 194--209 (2019; Zbl 1506.65244) Full Text: DOI
Colbrook, Matthew J.; Flyer, Natasha; Fornberg, Bengt On the Fokas method for the solution of elliptic problems in both convex and non-convex polygonal domains. (English) Zbl 1416.65472 J. Comput. Phys. 374, 996-1016 (2018). MSC: 65N35 35J05 65-04 PDFBibTeX XMLCite \textit{M. J. Colbrook} et al., J. Comput. Phys. 374, 996--1016 (2018; Zbl 1416.65472) Full Text: DOI Link
Grylonakis, Eleftherios-Nektarios G.; Filelis-Papadopoulos, Christos K.; Gravvanis, George A. A hybrid method for solving inhomogeneous elliptic PDEs based on Fokas method. (English) Zbl 1417.65191 Comput. Methods Appl. Math. 18, No. 4, 653-672 (2018). MSC: 65N22 65N35 65R10 35J05 37K10 PDFBibTeX XMLCite \textit{E.-N. G. Grylonakis} et al., Comput. Methods Appl. Math. 18, No. 4, 653--672 (2018; Zbl 1417.65191) Full Text: DOI
Grylonakis, E. N. G.; Filelis-Papadopoulos, C. K.; Gravvanis, G. A. A class of unified transform techniques for solving linear elliptic PDEs in convex polygons. (English) Zbl 1394.65154 Appl. Numer. Math. 129, 159-180 (2018). MSC: 65N35 35J60 35J15 35J05 65N80 PDFBibTeX XMLCite \textit{E. N. G. Grylonakis} et al., Appl. Numer. Math. 129, 159--180 (2018; Zbl 1394.65154) Full Text: DOI
Colbrook, Matthew J.; Fokas, Athanasisos S. Computing eigenvalues and eigenfunctions of the Laplacian for convex polygons. (English) Zbl 1380.65351 Appl. Numer. Math. 126, 1-17 (2018). MSC: 65N25 35P15 65N12 65N35 35J05 PDFBibTeX XMLCite \textit{M. J. Colbrook} and \textit{A. S. Fokas}, Appl. Numer. Math. 126, 1--17 (2018; Zbl 1380.65351) Full Text: DOI
Ashton, A. C. L.; Crooks, K. M. Numerical analysis of Fokas’ unified method for linear elliptic PDEs. (English) Zbl 1336.65183 Appl. Numer. Math. 104, 120-132 (2016). MSC: 65N22 35J25 65N25 35P30 47J10 65J15 65N30 65N38 PDFBibTeX XMLCite \textit{A. C. L. Ashton} and \textit{K. M. Crooks}, Appl. Numer. Math. 104, 120--132 (2016; Zbl 1336.65183) Full Text: DOI
Crowdy, Darren Fourier-Mellin transforms for circular domains. (English) Zbl 1331.44001 Comput. Methods Funct. Theory 15, No. 4, 655-687 (2015). MSC: 44A15 42A38 35A22 35J05 PDFBibTeX XMLCite \textit{D. Crowdy}, Comput. Methods Funct. Theory 15, No. 4, 655--687 (2015; Zbl 1331.44001) Full Text: DOI
Ashton, A. C. L.; Fokas, A. S. Elliptic equations with low regularity boundary data via the unified method. (English) Zbl 1318.35014 Complex Var. Elliptic Equ. 60, No. 5, 596-619 (2015). MSC: 35J25 35D30 35J05 PDFBibTeX XMLCite \textit{A. C. L. Ashton} and \textit{A. S. Fokas}, Complex Var. Elliptic Equ. 60, No. 5, 596--619 (2015; Zbl 1318.35014) Full Text: DOI arXiv
Dimakos, M.; Fokas, A. S. The Poisson and the biharmonic equations in the interior of a convex polygon. (English) Zbl 1318.35005 Stud. Appl. Math. 134, No. 4, 456-498 (2015). MSC: 35J05 35C15 PDFBibTeX XMLCite \textit{M. Dimakos} and \textit{A. S. Fokas}, Stud. Appl. Math. 134, No. 4, 456--498 (2015; Zbl 1318.35005) Full Text: DOI
Fokas, A. S.; Kalimeris, K. Eigenvalues for the Laplace operator in the interior of an equilateral triangle. (English) Zbl 1323.35108 Comput. Methods Funct. Theory 14, No. 1, 1-33 (2014). Reviewer: Claudia Simionescu-Badea (Wien) MSC: 35P05 35J05 PDFBibTeX XMLCite \textit{A. S. Fokas} and \textit{K. Kalimeris}, Comput. Methods Funct. Theory 14, No. 1, 1--33 (2014; Zbl 1323.35108) Full Text: DOI
Davis, Christopher-Ian Raphaël; Fornberg, Bengt A spectrally accurate numerical implementation of the Fokas transform method for Helmholtz-type PDEs. (English) Zbl 1291.65083 Complex Var. Elliptic Equ. 59, No. 4, 564-577 (2014). MSC: 65E05 65R10 35C15 31A10 35J25 PDFBibTeX XMLCite \textit{C.-I. R. Davis} and \textit{B. Fornberg}, Complex Var. Elliptic Equ. 59, No. 4, 564--577 (2014; Zbl 1291.65083) Full Text: DOI
Ashton, A. C. L. On the rigorous foundations of the Fokas method for linear elliptic partial differential equations. (English) Zbl 1364.35087 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 468, No. 2141, 1325-1331 (2012). MSC: 35J25 35C15 35J05 35A25 PDFBibTeX XMLCite \textit{A. C. L. Ashton}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 468, No. 2141, 1325--1331 (2012; Zbl 1364.35087) Full Text: DOI
Saridakis, Y. G.; Sifalakis, A. G.; Papadopoulou, E. P. Efficient numerical solution of the generalized Dirichlet-Neumann map for linear elliptic PDEs in regular polygon domains. (English) Zbl 1244.65191 J. Comput. Appl. Math. 236, No. 9, 2515-2528 (2012). Reviewer: Adrian Carabineanu (Bucureşti) MSC: 65N35 65T50 35J05 PDFBibTeX XMLCite \textit{Y. G. Saridakis} et al., J. Comput. Appl. Math. 236, No. 9, 2515--2528 (2012; Zbl 1244.65191) Full Text: DOI
Fornberg, Bengt; Flyer, Natasha A numerical implementation of Fokas boundary integral approach: Laplace’s equation on a polygonal domain. (English) Zbl 1226.65099 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 467, No. 2134, 2983-3003 (2011). MSC: 65N38 35J05 PDFBibTeX XMLCite \textit{B. Fornberg} and \textit{N. Flyer}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 467, No. 2134, 2983--3003 (2011; Zbl 1226.65099) Full Text: DOI
Pinotsis, D. A. Integral representations of displacements in linear elasticity. (English) Zbl 1223.35111 Appl. Math. Lett. 24, No. 10, 1670-1675 (2011). MSC: 35C15 74G05 PDFBibTeX XMLCite \textit{D. A. Pinotsis}, Appl. Math. Lett. 24, No. 10, 1670--1675 (2011; Zbl 1223.35111) Full Text: DOI
Charalambopoulos, A.; Dassios, G.; Fokas, A. S. Laplace’s equation in the exterior of a convex polygon. The equilateral triangle. (English) Zbl 1214.35013 Q. Appl. Math. 68, No. 4, 645-660 (2010). Reviewer: Lubomira Softova (Aversa) MSC: 35J05 35C15 35J25 31A25 31A10 PDFBibTeX XMLCite \textit{A. Charalambopoulos} et al., Q. Appl. Math. 68, No. 4, 645--660 (2010; Zbl 1214.35013) Full Text: DOI Link
Sifalakis, A. G.; Fulton, S. R.; Papadopoulou, E. P.; Saridakis, Y. G. Direct and iterative solution of the generalized Dirichlet-Neumann map for elliptic PDEs on square domains. (English) Zbl 1183.65154 J. Comput. Appl. Math. 227, No. 1, 171-184 (2009). Reviewer: Petr Necesal (Plzen) MSC: 65N35 35J25 35J05 65F05 65F10 PDFBibTeX XMLCite \textit{A. G. Sifalakis} et al., J. Comput. Appl. Math. 227, No. 1, 171--184 (2009; Zbl 1183.65154) Full Text: DOI
Fokas, A. S.; Flyer, N.; Smitheman, S. A.; Spence, E. A. A semi-analytical numerical method for solving evolution and elliptic partial differential equations. (English) Zbl 1170.65079 J. Comput. Appl. Math. 227, No. 1, 59-74 (2009). Reviewer: Michael Jung (Dresden) MSC: 65M70 65N38 35J25 35J65 35K15 35K55 PDFBibTeX XMLCite \textit{A. S. Fokas} et al., J. Comput. Appl. Math. 227, No. 1, 59--74 (2009; Zbl 1170.65079) Full Text: DOI