{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T18:09:53Z","timestamp":1779905393454,"version":"3.53.1"},"reference-count":55,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,5,5]],"date-time":"2025-05-05T00:00:00Z","timestamp":1746403200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2025,5,5]],"date-time":"2025-05-05T00:00:00Z","timestamp":1746403200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"DOI":"10.13039\/501100004052","name":"King Abdullah University of Science and Technology","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004052","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004052","name":"King Abdullah University of Science and Technology","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100004052","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2025,6]]},"DOI":"10.1007\/s10915-025-02898-x","type":"journal-article","created":{"date-parts":[[2025,5,5]],"date-time":"2025-05-05T04:35:21Z","timestamp":1746419721000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Traveling-Wave Solutions and Structure-Preserving Numerical Methods for a Hyperbolic Approximation of the Korteweg-de Vries Equation"],"prefix":"10.1007","volume":"103","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0741-6303","authenticated-orcid":false,"given":"Abhijit","family":"Biswas","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"I. Ketcheson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hendrik","family":"Ranocha","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jochen","family":"Sch\u00fctz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,5,5]]},"reference":[{"key":"2898_CR1","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1016\/j.cam.2014.01.015","volume":"266","author":"J \u00c1lvarez","year":"2014","unstructured":"\u00c1lvarez, J., Dur\u00e1n, A.: Petviashvili type methods for traveling wave computations: I. Analysis of convergence. J. Comput. Appl. Math. 266, 39\u201351 (2014)","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"2898_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1111\/j.1467-9590.2008.00422.x","volume":"122","author":"M Antuono","year":"2009","unstructured":"Antuono, M., Liapidevskii, V., Brocchini, M.: Dispersive nonlinear shallow-water equations. Stud. Appl. Math. 122(1), 1\u201328 (2009)","journal-title":"Stud. Appl. Math."},{"key":"2898_CR3","doi-asserted-by":"publisher","DOI":"10.1016\/j.compfluid.2020.104716","volume":"212","author":"C Bassi","year":"2020","unstructured":"Bassi, C., Bonaventura, L., Busto, S., Dumbser, M.: A hyperbolic reformulation of the Serre-Green-Naghdi model for general bottom topographies. Comput. Fluids 212, 104716 (2020)","journal-title":"Comput. Fluids"},{"issue":"3","key":"2898_CR4","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1007\/s42286-022-00069-1","volume":"4","author":"C Besse","year":"2022","unstructured":"Besse, C., Gavrilyuk, S., Kazakova, M., Noble, P.: Perfectly matched layers methods for mixed hyperbolic-dispersive equations. Water Waves 4(3), 313\u2013343 (2022)","journal-title":"Water Waves"},{"issue":"1","key":"2898_CR5","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1137\/141000671","volume":"59","author":"J Bezanson","year":"2017","unstructured":"Bezanson, J., Edelman, A., Karpinski, S., Shah, V.B.: Julia: a fresh approach to numerical computing. SIAM Rev. 59(1), 65\u201398 (2017). https:\/\/doi.org\/10.1137\/141000671","journal-title":"SIAM Rev."},{"issue":"6","key":"2898_CR6","doi-asserted-by":"publisher","first-page":"A3827","DOI":"10.1137\/23M1598118","volume":"46","author":"A Biswas","year":"2024","unstructured":"Biswas, A., Ketcheson, D.I.: Accurate solution of the nonlinear Schr\u00f6dinger equation via conservative multiple-relaxation ImEx methods. SIAM J. Sci. Comput. 46(6), A3827\u2013A3848 (2024). https:\/\/doi.org\/10.1137\/23M1598118","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"2898_CR7","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1007\/s10915-023-02312-4","volume":"97","author":"A Biswas","year":"2023","unstructured":"Biswas, A., Ketcheson, D.I.: Multiple-relaxation Runge Kutta methods for conservative dynamical systems. J. Sci. Comput. 97(1), 4 (2023)","journal-title":"J. Sci. Comput."},{"key":"2898_CR8","doi-asserted-by":"publisher","unstructured":"Biswas, A., Ketcheson, D.I., Ranocha, H., Sch\u00fctz, J.: Reproducibility repository for \u201cTraveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation\u201d. https:\/\/github.com\/abhibsws\/2024_kdvh_RR (2024). https:\/\/doi.org\/10.5281\/zenodo.14423351","DOI":"10.5281\/zenodo.14423351"},{"issue":"1","key":"2898_CR9","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s40324-024-00351-x","volume":"81","author":"S Boscarino","year":"2024","unstructured":"Boscarino, S., Russo, G.: Asymptotic preserving methods for quasilinear hyperbolic systems with stiff relaxation: a review. SeMA J. 81(1), 3\u201349 (2024)","journal-title":"SeMA J."},{"key":"2898_CR10","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/s13324-017-0163-y","volume":"8","author":"MK Brun","year":"2018","unstructured":"Brun, M.K., Kalisch, H.: Convective wave breaking in the KdV equation. Anal. Math. Phys. 8, 57\u201375 (2018)","journal-title":"Anal. Math. Phys."},{"key":"2898_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0065-2156(08)70254-0","volume":"31","author":"R Camassa","year":"1994","unstructured":"Camassa, R., Holm, D.D., Hyman, J.M.: A new integrable shallow water equation. Adv. Appl. Mech. 31, 1\u201333 (1994)","journal-title":"Adv. Appl. Mech."},{"issue":"7","key":"2898_CR12","doi-asserted-by":"publisher","DOI":"10.1063\/5.0151928","volume":"35","author":"A Chesnokov","year":"2023","unstructured":"Chesnokov, A., Ermishina, V., Liapidevskii, V.Y.: Strongly non-linear Boussinesq-type model of the dynamics of internal solitary waves propagating in a multilayer stratified fluid. Phys. Fluids 35(7), 076605 (2023)","journal-title":"Phys. Fluids"},{"key":"2898_CR13","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/j.compfluid.2019.05.017","volume":"189","author":"A Chesnokov","year":"2019","unstructured":"Chesnokov, A., Nguyen, T.H.: Hyperbolic model for free surface shallow water flows with effects of dispersion, vorticity and topography. Comput. Fluids 189, 13\u201323 (2019)","journal-title":"Comput. Fluids"},{"issue":"2","key":"2898_CR14","doi-asserted-by":"publisher","DOI":"10.1063\/1.1845603","volume":"46","author":"A Constantin","year":"2005","unstructured":"Constantin, A.: Finite propagation speed for the Camassa-Holm equation. J. Math. Phys. 46(2), 023506 (2005)","journal-title":"J. Math. Phys."},{"key":"2898_CR15","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1007\/s00205-008-0128-2","volume":"192","author":"A Constantin","year":"2009","unstructured":"Constantin, A., Lannes, D.: The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations. Arch. Ration. Mech. Anal. 192, 165\u2013186 (2009)","journal-title":"Arch. Ration. Mech. Anal."},{"issue":"65","key":"2898_CR16","doi-asserted-by":"publisher","first-page":"3349","DOI":"10.21105\/joss.03349","volume":"6","author":"S Danisch","year":"2021","unstructured":"Danisch, S., Krumbiegel, J.: Makie.jl: flexible high-performance data visualization for Julia. J. Open Source Softw. 6(65), 3349 (2021). https:\/\/doi.org\/10.21105\/joss.03349","journal-title":"J. Open Source Softw."},{"issue":"4","key":"2898_CR17","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1007\/s002110050247","volume":"75","author":"J De Frutos","year":"1997","unstructured":"De Frutos, J., Sanz-Serna, J.M.: Accuracy and conservation properties in numerical integration: the case of the Korteweg-de Vries equation. Numer. Math. 75(4), 421\u2013445 (1997). https:\/\/doi.org\/10.1007\/s002110050247","journal-title":"Numer. Math."},{"key":"2898_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2022.111544","volume":"470","author":"F Dhaouadi","year":"2022","unstructured":"Dhaouadi, F., Dumbser, M.: A first order hyperbolic reformulation of the Navier-Stokes-Korteweg system based on the GPR model and an augmented Lagrangian approach. J. Comput. Phys. 470, 111544 (2022)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"2898_CR19","doi-asserted-by":"publisher","first-page":"336","DOI":"10.1111\/sapm.12238","volume":"142","author":"F Dhaouadi","year":"2019","unstructured":"Dhaouadi, F., Favrie, N., Gavrilyuk, S.: Extended Lagrangian approach for the defocusing nonlinear Schr\u00f6dinger equation. Stud. Appl. Math. 142(3), 336\u2013358 (2019)","journal-title":"Stud. Appl. Math."},{"key":"2898_CR20","volume":"433","author":"F Dhaouadi","year":"2022","unstructured":"Dhaouadi, F., Gavrilyuk, S., Vila, J.P.: Hyperbolic relaxation models for thin films down an inclined plane. Appl. Math. Comput. 433, 127378 (2022)","journal-title":"Appl. Math. Comput."},{"issue":"6","key":"2898_CR21","doi-asserted-by":"publisher","first-page":"1547","DOI":"10.1088\/0951-7715\/11\/6\/008","volume":"11","author":"A Dur\u00e1n","year":"1998","unstructured":"Dur\u00e1n, A., Sanz-Serna, J.M.: The numerical integration of relative equilibrium solutions. Geometric theory. Nonlinearity 11(6), 1547 (1998). https:\/\/doi.org\/10.1088\/0951-7715\/11\/6\/008","journal-title":"Nonlinearity"},{"issue":"2","key":"2898_CR22","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1093\/imanum\/20.2.235","volume":"20","author":"A Dur\u00e1n","year":"2000","unstructured":"Dur\u00e1n, A., Sanz-Serna, J.M.: The numerical integration of relative equilibrium solutions. The nonlinear Schr\u00f6dinger equation. IMA J. Numer. Anal. 20(2), 235\u2013261 (2000). https:\/\/doi.org\/10.1093\/imanum\/20.2.235","journal-title":"IMA J. Numer. Anal."},{"key":"2898_CR23","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1016\/j.jcp.2019.05.035","volume":"394","author":"C Escalante","year":"2019","unstructured":"Escalante, C., Dumbser, M., Castro, M.J.: An efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution with high order discontinuous Galerkin schemes. J. Comput. Phys. 394, 385\u2013416 (2019)","journal-title":"J. Comput. Phys."},{"issue":"7","key":"2898_CR24","doi-asserted-by":"publisher","first-page":"2718","DOI":"10.1088\/1361-6544\/aa712d","volume":"30","author":"N Favrie","year":"2017","unstructured":"Favrie, N., Gavrilyuk, S.: A rapid numerical method for solving Serre-Green-Naghdi equations describing long free surface gravity waves. Nonlinearity 30(7), 2718 (2017)","journal-title":"Nonlinearity"},{"key":"2898_CR25","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1016\/j.compfluid.2014.02.016","volume":"95","author":"DCDR Fern\u00e1ndez","year":"2014","unstructured":"Fern\u00e1ndez, D.C.D.R., Hicken, J.E., Zingg, D.W.: Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations. Comput. Fluids 95, 171\u2013196 (2014). https:\/\/doi.org\/10.1016\/j.compfluid.2014.02.016","journal-title":"Comput. Fluids"},{"issue":"2","key":"2898_CR26","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1109\/JPROC.2004.840301","volume":"93","author":"M Frigo","year":"2005","unstructured":"Frigo, M., Johnson, S.G.: The design and implementation of FFTW3. Proc. IEEE 93(2), 216\u2013231 (2005). https:\/\/doi.org\/10.1109\/JPROC.2004.840301","journal-title":"Proc. IEEE"},{"key":"2898_CR27","doi-asserted-by":"crossref","unstructured":"Gavrilyuk, S., Nkonga, B., Shyue, K.M.: The conduit equation: Hyperbolic approximation and generalized Riemann problem. Available at SSRN 4724161 (2024)","DOI":"10.2139\/ssrn.4724161"},{"issue":"3","key":"2898_CR28","doi-asserted-by":"publisher","first-page":"1447","DOI":"10.1088\/1361-6544\/ac4c49","volume":"35","author":"S Gavrilyuk","year":"2022","unstructured":"Gavrilyuk, S., Shyue, K.M.: Hyperbolic approximation of the BBM equation. Nonlinearity 35(3), 1447 (2022)","journal-title":"Nonlinearity"},{"key":"2898_CR29","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/s10665-009-9328-5","volume":"67","author":"G Grosso","year":"2010","unstructured":"Grosso, G., Antuono, M., Brocchini, M.: Dispersive nonlinear shallow-water equations: some preliminary numerical results. J. Eng. Math. 67, 71\u201384 (2010)","journal-title":"J. Eng. Math."},{"issue":"7825","key":"2898_CR30","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1038\/s41586-020-2649-2","volume":"585","author":"CR Harris","year":"2020","unstructured":"Harris, C.R., Millman, K.J., Van Der Walt, S.J., Gommers, R., Virtanen, P., Cournapeau, D., Wieser, E., Taylor, J., Berg, S., Smith, N.J., Kern, R., Picus, M., Hoyer, S., van Kerkwijk, M.H., Brett, M., Haldane, A., Del R\u00edo, J.F., Wiebe, M., Peterson, P., G\u00e9rard-Marchant, P., Sheppard, K., Reddy, T., Weckesser, W., Abbasi, H., Gohlke, C., Oliphant, T.E.: Array programming with NumPy. Nature 585(7825), 357\u2013362 (2020). https:\/\/doi.org\/10.1038\/s41586-020-2649-2","journal-title":"Nature"},{"issue":"3","key":"2898_CR31","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1109\/MCSE.2007.55","volume":"9","author":"JD Hunter","year":"2007","unstructured":"Hunter, J.D.: Matplotlib: a 2D graphics environment. Comput. Sci. Eng. 9(3), 90\u201395 (2007). https:\/\/doi.org\/10.1109\/MCSE.2007.55","journal-title":"Comput. Sci. Eng."},{"key":"2898_CR32","first-page":"177","volume":"3","author":"S Jin","year":"2012","unstructured":"Jin, S.: Asymptotic preserving (AP) schemes for multiscale kinetic and hyperbolic equations: a review. Riv. Mat. Della Univ. Parma 3, 177\u2013216 (2012)","journal-title":"Riv. Mat. Della Univ. Parma"},{"key":"2898_CR33","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1017\/S0962492922000010","volume":"31","author":"S Jin","year":"2022","unstructured":"Jin, S.: Asymptotic-preserving schemes for multiscale physical problems. Acta Numer. 31, 415\u2013489 (2022). https:\/\/doi.org\/10.1017\/S0962492922000010","journal-title":"Acta Numer."},{"issue":"1\u20132","key":"2898_CR34","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1016\/S0168-9274(02)00138-1","volume":"44","author":"CA Kennedy","year":"2003","unstructured":"Kennedy, C.A., Carpenter, M.H.: Additive Runge-Kutta schemes for convection-diffusion-reaction equations. Appl. Numer. Math. 44(1\u20132), 139\u2013181 (2003)","journal-title":"Appl. Numer. Math."},{"issue":"6","key":"2898_CR35","doi-asserted-by":"publisher","first-page":"2850","DOI":"10.1137\/19M1263662","volume":"57","author":"DI Ketcheson","year":"2019","unstructured":"Ketcheson, D.I.: Relaxation Runge-Kutta methods: conservation and stability for inner-product norms. SIAM J. Numer. Anal. 57(6), 2850\u20132870 (2019)","journal-title":"SIAM J. Numer. Anal."},{"issue":"5","key":"2898_CR36","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6544\/adc6e8","volume":"38","author":"DI Ketcheson","year":"2025","unstructured":"Ketcheson, D.I., Biswas, A.: Approximation of arbitrarily high-order pdes by first-order hyperbolic relaxation. Nonlinearity 38(5), 055002 (2025). https:\/\/doi.org\/10.1088\/1361-6544\/adc6e8","journal-title":"Nonlinearity"},{"issue":"1","key":"2898_CR37","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1016\/j.jmaa.2004.11.038","volume":"306","author":"J Lenells","year":"2005","unstructured":"Lenells, J.: Traveling wave solutions of the Degasperis-Procesi equation. J. Math. Anal. Appl. 306(1), 72\u201382 (2005)","journal-title":"J. Math. Anal. Appl."},{"key":"2898_CR38","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3766","author":"D Li","year":"2022","unstructured":"Li, D., Li, X., Zhang, Z.: Implicit-explicit relaxation Runge-Kutta methods: construction, analysis and applications to PDEs. Math. Comput. (2022). https:\/\/doi.org\/10.1090\/mcom\/3766","journal-title":"Math. Comput."},{"key":"2898_CR39","doi-asserted-by":"crossref","unstructured":"Li, L., Lou, J., Luo, H., Nishikawa, H.: A new formulation of hyperbolic Navier-Stokes solver based on finite volume method on arbitrary grids. In: 2018 Fluid Dynamics Conference, p. 4160 (2018)","DOI":"10.2514\/6.2018-4160"},{"key":"2898_CR40","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1016\/j.jcp.2017.01.042","volume":"335","author":"K Mattsson","year":"2017","unstructured":"Mattsson, K.: Diagonal-norm upwind SBP operators. J. Comput. Phys. 335, 283\u2013310 (2017). https:\/\/doi.org\/10.1016\/j.jcp.2017.01.042","journal-title":"J. Comput. Phys."},{"issue":"Supplement C","key":"2898_CR41","doi-asserted-by":"publisher","first-page":"593","DOI":"10.1016\/j.jcp.2016.06.001","volume":"321","author":"A Mazaheri","year":"2016","unstructured":"Mazaheri, A., Ricchiuto, M., Nishikawa, H.: A first-order hyperbolic system approach for dispersion. J. Comput. Phys. 321(Supplement C), 593\u2013605 (2016)","journal-title":"J. Comput. Phys."},{"key":"2898_CR42","first-page":"129","volume":"25","author":"L Pareschi","year":"2005","unstructured":"Pareschi, L., Russo, G.: Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation. J. Sci. Comput. 25, 129\u2013155 (2005)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"2898_CR43","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1007\/s10543-018-0736-7","volume":"59","author":"H Ranocha","year":"2019","unstructured":"Ranocha, H.: Mimetic properties of difference operators: product and chain rules as for functions of bounded variation and entropy stability of second derivatives. BIT Numer. Math. 59(2), 547\u2013563 (2019). https:\/\/doi.org\/10.1007\/s10543-018-0736-7","journal-title":"BIT Numer. Math."},{"issue":"64","key":"2898_CR44","doi-asserted-by":"publisher","first-page":"3454","DOI":"10.21105\/joss.03454","volume":"6","author":"H Ranocha","year":"2021","unstructured":"Ranocha, H.: SummationByPartsOperators.jl: a Julia library of provably stable semidiscretization techniques with mimetic properties. J. Open Source Softw. 6(64), 3454 (2021). https:\/\/doi.org\/10.21105\/joss.03454","journal-title":"J. Open Source Softw."},{"key":"2898_CR45","doi-asserted-by":"publisher","first-page":"875","DOI":"10.1007\/s00211-020-01158-4","volume":"146","author":"H Ranocha","year":"2020","unstructured":"Ranocha, H., L\u00f3czi, L., Ketcheson, D.I.: General relaxation methods for initial-value problems with application to multistep schemes. Numer. Math. 146, 875\u2013906 (2020). https:\/\/doi.org\/10.1007\/s00211-020-01158-4","journal-title":"Numer. Math."},{"issue":"4","key":"2898_CR46","doi-asserted-by":"publisher","first-page":"979","DOI":"10.4208\/cicp.OA-2020-0119","volume":"29","author":"H Ranocha","year":"2021","unstructured":"Ranocha, H., Mitsotakis, D., Ketcheson, D.I.: A broad class of conservative numerical methods for dispersive wave equations. Commun. Comput. Phys. 29(4), 979\u20131029 (2021). https:\/\/doi.org\/10.4208\/cicp.OA-2020-0119","journal-title":"Commun. Comput. Phys."},{"issue":"2","key":"2898_CR47","doi-asserted-by":"publisher","first-page":"A612","DOI":"10.1137\/19M1263480","volume":"42","author":"H Ranocha","year":"2020","unstructured":"Ranocha, H., Sayyari, M., Dalcin, L., Parsani, M., Ketcheson, D.I.: Relaxation Runge-Kutta methods: fully-discrete explicit entropy-stable schemes for the compressible Euler and Navier-Stokes equations. SIAM J. Sci. Comput. 42(2), A612\u2013A638 (2020). https:\/\/doi.org\/10.1137\/19M1263480","journal-title":"SIAM J. Sci. Comput."},{"key":"2898_CR48","volume-title":"Difference Methods for Boundary-Value Problems","author":"RD Richtmyer","year":"1967","unstructured":"Richtmyer, R.D., Morton, K.W.: Difference Methods for Boundary-Value Problems. Wiley, New York, London, Sydney (1967)"},{"issue":"8","key":"2898_CR49","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.98.084044","volume":"98","author":"HR R\u00fcter","year":"2018","unstructured":"R\u00fcter, H.R., Hilditch, D., Bugner, M., Br\u00fcgmann, B.: Hyperbolic relaxation method for elliptic equations. Phys. Rev. D 98(8), 084044 (2018)","journal-title":"Phys. Rev. D"},{"issue":"2","key":"2898_CR50","doi-asserted-by":"publisher","first-page":"522","DOI":"10.1007\/s10915-014-9942-x","volume":"64","author":"J Sch\u00fctz","year":"2015","unstructured":"Sch\u00fctz, J., Noelle, S.: Flux splitting for stiff equations: a notion on stability. J. Sci. Comput. 64(2), 522\u2013540 (2015)","journal-title":"J. Sci. Comput."},{"key":"2898_CR51","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/j.jcp.2014.02.031","volume":"268","author":"M Sv\u00e4rd","year":"2014","unstructured":"Sv\u00e4rd, M., Nordstr\u00f6m, J.: Review of summation-by-parts schemes for initial-boundary-value problems. J. Comput. Phys. 268, 17\u201338 (2014). https:\/\/doi.org\/10.1016\/j.jcp.2014.02.031","journal-title":"J. Comput. Phys."},{"issue":"5","key":"2898_CR52","doi-asserted-by":"publisher","first-page":"A2423","DOI":"10.1137\/130937469","volume":"36","author":"EF Toro","year":"2014","unstructured":"Toro, E.F., Montecinos, G.I.: Advection-diffusion-reaction equations: hyperbolization and high-order ADER discretizations. SIAM J. Sci. Comput. 36(5), A2423\u2013A2457 (2014)","journal-title":"SIAM J. Sci. Comput."},{"key":"2898_CR53","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","volume":"17","author":"P Virtanen","year":"2020","unstructured":"Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Jarrod Millman, K., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C., Polat, I., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P.: SciPy 1.0 contributors: SciPy 1.0: fundamental algorithms for scientific computing in python. Nat. Methods 17, 261\u2013272 (2020). https:\/\/doi.org\/10.1038\/s41592-019-0686-2","journal-title":"Nat. Methods"},{"key":"2898_CR54","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719680","volume-title":"Nonlinear Waves in Integrable and Nonintegrable Systems","author":"J Yang","year":"2010","unstructured":"Yang, J.: Nonlinear Waves in Integrable and Nonintegrable Systems. SIAM, Philadelphia (2010)"},{"key":"2898_CR55","doi-asserted-by":"publisher","first-page":"292","DOI":"10.4208\/cicp.OA-2018-0270","volume":"27","author":"J Zeifang","year":"2020","unstructured":"Zeifang, J., Sch\u00fctz, J., Kaiser, K., Beck, A., Luk\u00e1\u010dov\u00e1-Medvid\u2019ov\u00e1, M., Noelle, S.: A novel full-Euler low Mach number IMEX splitting. Commun. Comput. Phys. 27, 292\u2013320 (2020)","journal-title":"Commun. Comput. Phys."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-025-02898-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-025-02898-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-025-02898-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,23]],"date-time":"2025-05-23T13:18:53Z","timestamp":1748006333000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-025-02898-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,5]]},"references-count":55,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["2898"],"URL":"https:\/\/doi.org\/10.1007\/s10915-025-02898-x","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,5]]},"assertion":[{"value":"23 December 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 March 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 March 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 May 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"On behalf of all authors, the corresponding author declares that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"90"}}