[1] A.A. Abramov, A.L. Dyshko, N.B. Konyukhova, T.V. Levitina, Computation of angular wave functions of Lame by means of solution of auxiliary differential equations, Comput. Math. Math. Phys. 29 (1989) 119–131.
[2] A.A. Abramov, V.I. Ul’yanova, A method for solving self-adjoint multiparameter spectral problems for weakly coupled sets of ordinary differential equations, Comput. Math. Math. Phys. 37 (1997) 552–557.
[3] P. Amodio, T. Levitina, G. Settani, E.B. Weinmuller, Numerical simulation of the whispering gallery modes in prolate spheriods, Comput. Phys. Commun. 185 (2014) 1200–1206.
[4] F.M. Arscott, P.J. Taylor, R.V.M. Zahar, On the numerical construction of ellipsoidal wave functions, Math. Comp. 40 (1983) 367–380.
[5] F.V. Atkinson, Multiparameter Eigenvalue Problems, Academic Press, New York, 1972.
[6] F.V. Atkinson, A.B. Mingarelli, Multiparameter Eigenvalue Problems. Sturm–Liouville Theory, CRC Press, Boca Raton, 2010.
[7] P.B. Bailey, The automatic solution of two-parameter Sturm-Liouville eigenvalue problems in ordinary differential equations, Appl. Math. Comput. 8 (1981) 251–259.
[8] R.H. Bartels, G. W. Stewart, Algorithm 432: Solution of matrix equation AX + XB = C, Comm. ACM 15 (1972) 820–826.
[9] J. Boersma, J.K.M. Jansen, Electromagnetic field singularities at the tip of an elliptic cone, EUT Report 90-WSK-Ol, TU Eindhoven, 1991.
[10] J.P. Boyd, Chebyshev and Fourier Spectral Methods, 2nd ed., Dover Publications, Mineola, 2001.
[11] J.P. Boyd, Chebyshev spectral methods and the Lane-Emden problem, Numer. Math. Theor. Meth. Appl. 4 (2011) 142–157.
[12] M. Faierman, Two-parameter Eigenvalue Problems in Ordinary Differential Equations, volume 205 of Pitman Research Notes in Mathematics Series, Longman Scientific and Technical, Harlow, 1991.
[13] B. Fornberg, A Practical Guide to Pseudospectral Methods, Cambridge University Press, Cambridge, 1998.
[14] C.I. Gheorghiu, Spectral Methods for Differential Problems, Casa Cartii de Stiinta, Cluj-Napoca, 2007.
[15] C.I. Gheorghiu, Spectral Methods for Non-Standard Eigenvalue Problems. Fluid and Structural Mechanics and Beyond, Springer, Cham, Heidelberg, New York, Dordrecht, London, 2014.
[16] C.I. Gheorghiu, M.E. Hochstenbach, B. Plestenjak, J. Rommes, Spectral collocation solutions to multiparameter Mathieu’s system, Appl. Math. Comp. 218 (2012) 11990–12000.
[17] G.H. Golub, C.F. Van Loan, Matrix Computations, 3rd ed., The Johns Hopkins University Press, Baltimore, 1996.
[18] D. Gottlieb, S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM, Philadelphia, 1977.
[19] M.E. Hochstenbach, T. Kosir, B. Plestenjak. A Jacobi–Davidson type method for the nonsingular two-parameter eigenvalue problem, SIAM J. Matrix Anal. Appl. 26 (2005) 477–497.
[20] M. E. Hochstenbach, B. Plestenjak, Harmonic Rayleigh-Ritz for the multiparameter eigenvalue problem, Elec. Trans. Numer. Anal. 29 (2008) 81–96.
[21] J. Hoepffner, Implementation of boundary conditions, www.fukagata.mech.keio.ac.jp/~jerome/ (2007).
[22] X. Ji, On 2D bisection method for double eigenvalue problems, J. Comp. Phys. 126 (1996) 91–98.
[23] E.D. Kalinin, Modification of a method for solving the multiparameter eigenvalue problem for systems of loosely coupled ordinary differential equations, Comput. Math. Math. Phys. 53 (2013) 874–881.
[24] L. Kraus, L. Levine, Diffraction by an elliptic cone, Commun. Pure Appl. Math. 9 (1961), 49–68.
[25] J. R. Kuttler, V. G. Sigillito, Eigenvalues of the Laplacian in two dimensions, SIAM Rev. 26 (1984) 163–193.
[26] T.V. Levitina, On numerical solution of multiparameter Sturm-Liouville spectral problems. Numerical analysis and mathematical modelling, Banach Center Publ., 29, Polish Acad. Sci., Warsaw, 1994, 275–281.
[27] T.V. Levitina, A numerical solution to some three-parameter spectral problems, Comput. Math. Math. Phys. 39 (1999) 1715–1729.
[28] L.C. Lew Yan Voon, M. Willatzen, Helmholtz equation in parabolic rotational coordinates: application to wave problems in quantum mechanics and acoustics, Math. Comp. Simul. 65 (2004) 337–349.
[29] K. Meerbergen, B. Plestenjak, A Sylvester–Arnoldi type method for the generalized eigenvalue problem with two-by-two operator determinants, Report TW 653, Department of Computer Science, KU Leuven, 2014, to appear in Numer. Linear Algebra Appl.
[30] P. Moon, D.E. Spencer, Field Theory Handbook, Springer-Verlag, New York, 1971.
[31] J.A. Morrison, J.A. Lewis, Charge singularity at the corner of a flat plate, SIAM J. Appl. Math. 31 (1976) 233–250.
[32] F.W.J. Olver (Ed.), NIST Handbook of Mathematical Functions, Cambridge University Press, Cambridge, 2010.
[33] S.H. Patil, Hydrogen molecular ion and molecule in two dimensions, J. Chem. Phys. 118 (2003) 2197–2205.
[34] B. Plestenjak, A continuation method for a right definite two-parameter eigenvalue problem, SIAM J. Matrix Anal. Appl. 21 (2000) 1163–1184.
[35] B. Plestenjak, MultiParEig, www.mathworks.com/matlabcentral/fileexchange/47844-multipareig, MATLAB Central File Exchange. Retrieved September 14, 2014.
[36] B.D. Sleeman, Multiparameter spectral theory and separation of variables, J. Phys. A: Math. Theor. 41 (2008) 1–20.
[37] D.C. Sorensen, Implicit application of polynomial filters in a k-step Arnoldi method, SIAM J. Matrix Anal. Appl. 13 (1992) 357–385.
[38] G.W. Stewart, A Krylov–Schur algorithm for large eigenproblems, SIAM J. Matrix Anal. Appl., 23 (2001), 601–614.
[39] T. Toolan, lapack, www.mathworks.com/matlabcentral/fileexchange/16777-lapack, MATLAB Central File Exchange. Retrieved August 20, 2014.
[40] L.N. Trefethen, Spectral Methods in MATLAB, SIAM, Philadelphia, 2000.
[41] H. Volkmer, Multiparameter Problems and Expansion Theorems, Lecture Notes in Math. 1356, Springer-Verlag, New York, 1988.
[42] J.A.C. Weideman, DMSUITE, www.mathworks.com/matlabcentral/fileexchange/29-dmsuite, MATLAB Central File Exchange. Retrieved August 20, 2014.
[43] J.A.C. Weideman, S.C. Reddy, A MATLAB differentiation matrix suite, ACM Trans. Math. Softw. 26 (2000) 465–519.
[44] M. Willatzen, L.C. Lew Yan Voon, Theory of acoustic eigenmodes in parabolic cylindrical enclosures, J. Sound Vib. 286 (2005) 251–264.
[45] M. Willatzen, L.C. Lew Yan Voon, Numerical implementation of the ellipsoidal wave equation and application to ellipsoidal quantum dots, Comput. Phys. Commun. 171 (2005) 1–18.
[46] M. Willatzen, L. C. Lew Yan Voon, Separable Boundary-Value Problems in Physics, WileyVCH, Weinheim, 2011.