Performance analysis of error-control B-spline Gaussian collocation software for PDEs

de Boor, 2001, A practical guide to splines Ascher, 1981, Collocation software for boundary value ODEs, ACM Trans. Math. Software, 7, 209, 10.1145/355945.355950 NAG Numerical Algorithms Group fortran library. d02tlf. in: The Numerical Algorithms Group, Ltd., Wilkinson House, Oxford, UK. Scilab, bvode, Scilab Enterprises, 143 bis rue Yves Le Coz, 78000 Versailles, France. P. Virtanen, Scikits.bvp1lg 0.2.8, https://pv.github.io/scikits.bvp1lg/. Brenan, 1996, Numerical solution of initial-value problems in differential-algebraic equations Madsen, 1979, Algorithm 540: PDECOL, general collocation software for partial differential equations, ACM Trans. Math. Software, 5, 326, 10.1145/355841.355849 Keast, 1991, Algorithm 688: EPDCOL: A more efficient PDECOL code, ACM Trans. Math. Software, 17, 153, 10.1145/108556.108558 Fairweather, 2004, Algorithms for almost block diagonal linear systems, SIAM Rev., 46, 49, 10.1137/S003614450240506X Díaz, 1983, Algorithm 603. COLROW and ARCECO: FORTRAN packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination, ACM Trans. Math. Software, 9, 376, 10.1145/356044.356054 Wang, 2004, BACOL: B-spline adaptive COL-location software for 1D parabolic PDEs, ACM Trans. Math. Software, 30, 454, 10.1145/1039813.1039817 Wang, 2004, A high-order global spatially adaptive collocation method for 1-D parabolic PDEs, Appl. Numer. Math., 50, 239, 10.1016/j.apnum.2003.12.023 Wang, 2008, Algorithm 874: BACOLR: Spatial and temporal error control software for PDEs based on high-order adaptive collocation, ACM Trans. Math. Software, 34, 15:1, 10.1145/1356052.1356056 Hairer, 1996, Solving ordinary differential equations. II Huang, 1996, A moving collocation method for solving time dependent partial differential equations, Appl. Numer. Math., 20, 101, 10.1016/0168-9274(95)00119-0 Moore, 2001, Interpolation error-based a posteriori error estimation for two-point boundary value problems and parabolic equations in one space dimension, Numer. Math., 90, 149, 10.1007/s002110100297 Wang, 2004, A comparison of adaptive software for 1D parabolic PDEs, J. Comput. Appl. Math., 169, 127, 10.1016/j.cam.2003.12.016 Pew, 2016, Algorithm 962: BACOLI: B-spline adaptive collocation software for PDEs with interpolation-based spatial error control, ACM Trans. Math. Software, 42, 25:1, 10.1145/2818312 Li, 2013, B-spline Gaussian collocation software for two-dimensional parabolic PDEs, Adv. Appl. Math. Mech., 5, 528, 10.4208/aamm.13-13S09 Huang, 2011, Adaptive moving mesh methods Muir, 2015, Tolerance vs. error results for a class of error control b-spline Gaussian collocation PDE solvers Pew, 2018, Performance analysis results for error control B-spline Gaussian collocation PDE solvers Arsenault, 2009, Superconvergent interpolants for efficient spatial error estimation in 1D PDE collocation solvers, Can. Appl. Math. Q., 17, 409 Arsenault, 2012, Asymptotically correct interpolation-based spatial error estimation for 1D PDE solvers, Can. Appl. Math. Q., 20, 307 Hairer, 1993, Solving ordinary differential equations. I Zhang, 1993, Diffusive effects on a catalytic surface reaction: An initial boundary value problem in reaction–diffusion-convection equations, J. Bifurc. Chaos, 3, 79, 10.1142/S0218127493000052