{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T11:47:44Z","timestamp":1769168864657,"version":"3.49.0"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2012,3,1]],"date-time":"2012-03-01T00:00:00Z","timestamp":1330560000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Earth Sci Inform"],"published-print":{"date-parts":[[2012,3]]},"DOI":"10.1007\/s12145-011-0093-4","type":"journal-article","created":{"date-parts":[[2012,3,6]],"date-time":"2012-03-06T08:08:12Z","timestamp":1331021292000},"page":"23-31","source":"Crossref","is-referenced-by-count":13,"title":["Application of new RKAHeM(4,4) technique to analyze the structure of initial extrasolar giant protoplanets"],"prefix":"10.1007","volume":"5","author":[{"given":"Sukumar","family":"Senthilkumar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gour Chandra","family":"Paul","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,3,7]]},"reference":[{"key":"93_CR1","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/0097-8485(87)80030-X","volume":"11","author":"M Bader","year":"1987","unstructured":"Bader M (1987) A comparative study of new truncation error estimates and intrinsic accuracies of some higher order Runge-Kutta algorithms. Comput Chem 11:121\u2013124","journal-title":"Comput Chem"},{"key":"93_CR2","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/s002140050328","volume":"99","author":"M Bader","year":"1998","unstructured":"Bader M (1998) A new technique for the early detection of stiffness in coupled differential equations and application to standard Runge\u2013Kutta algorithms. Theor Chem Acc 99:215\u2013219","journal-title":"Theor Chem Acc"},{"key":"93_CR3","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/0019-1035(80)90012-3","volume":"41","author":"P Bodenheimer","year":"1980","unstructured":"Bodenheimer P, Grossman AS, DeCampli WM, Marcy G, Pollack JB (1980) Calculations of the evolution of the giant planets. Icarus 41:293\u2013308","journal-title":"Icarus"},{"key":"93_CR4","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1016\/j.icarus.2010.01.015","volume":"207","author":"AC Boley","year":"2010","unstructured":"Boley AC, Hayfield T, Mayer L, Durisen RH (2010) Clumps in the outer disk by disk instability: why they are initially gas giants and the legacy of disruption. Icarus 207:509\u2013516","journal-title":"Icarus"},{"key":"93_CR5","doi-asserted-by":"crossref","first-page":"1836","DOI":"10.1126\/science.276.5320.1836","volume":"276","author":"AP Boss","year":"1997","unstructured":"Boss AP (1997) Giant planet formation by gravitational instability. Science 276:1836\u20131839","journal-title":"Science"},{"key":"93_CR6","doi-asserted-by":"crossref","unstructured":"Boss AP (1998) Evolution of the solar nebula. IV. Giant gaseous protoplanet formation. Astrophys J 503:923\u2013937","DOI":"10.1086\/306036"},{"key":"93_CR7","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1086\/341736","volume":"576","author":"AP Boss","year":"2002","unstructured":"Boss AP (2002) Evolution of the solar nebula. V. Disk instabilities with varied thermodynamics. Astrophys J 576:462\u2013472","journal-title":"Astrophys J"},{"key":"93_CR8","doi-asserted-by":"crossref","first-page":"L73","DOI":"10.1086\/518691","volume":"661","author":"AP Boss","year":"2007","unstructured":"Boss AP (2007) Testing disk instability models for giant planet formation. Astrophys J 661:L73\u2013L76","journal-title":"Astrophys J"},{"key":"93_CR9","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/0019-1035(79)90193-3","volume":"38","author":"WM DeCampli","year":"1979","unstructured":"DeCampli WM, Cameron AGW (1979) Structure and evolution of isolated giant gaseous protoplanets. Icarus 38:367\u2013391","journal-title":"Icarus"},{"key":"93_CR10","first-page":"607","volume-title":"Protostars and planets","author":"RH Durisen","year":"2007","unstructured":"Durisen RH, Boss AP, Mayer L, Nelson AF, Quinn T, Rice WKM (2007) In: Reipurth VB, Jewitt D, Keil K (eds) Protostars and planets. University of Arizona Press, Tucson, p 607"},{"key":"93_CR11","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1080\/00207169508804442","volume":"58","author":"DJ Evans","year":"1995","unstructured":"Evans DJ, Yaakub AR (1995) A new Runge\u2013Kutta RK(4, 4) technique. Int J Comput Math 58:169\u2013187","journal-title":"Int J Comput Math"},{"key":"93_CR12","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1080\/00207169508804437","volume":"58","author":"DJ Evans","year":"1995","unstructured":"Evans DJ, Yaacob N (1995) A fourth order Runge\u2013Kutta method based on the Heronian Mean formula. Int J Comput Math 58:103\u2013115","journal-title":"Int J Comput Math"},{"key":"93_CR13","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.icarus.2008.08.002","volume":"198","author":"R Helled","year":"2008","unstructured":"Helled R, Schubert G (2008) Core formation in giant gaseous protoplanets. Icarus 198:56\u2013162","journal-title":"Icarus"},{"key":"93_CR14","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1016\/j.icarus.2010.09.024","volume":"211","author":"R Helled","year":"2011","unstructured":"Helled R, Bodenheimer P (2011) The effects of metallicity and grain growth and settling on the early evolution of gaseous protoplanets. Icarus 211:939\u2013947","journal-title":"Icarus"},{"key":"93_CR15","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1016\/j.icarus.2005.06.021","volume":"179","author":"O Hubickyj","year":"2005","unstructured":"Hubickyj O, Bodenheimer P, Lissauer JJ (2005) Accretion of the gaseous envelope of Jupiter around a 5\u201310 Earth-mass core. Icarus 179:415\u2013431","journal-title":"Icarus"},{"key":"93_CR16","volume-title":"Computational methods in ordinary differential equations","author":"JD Lambert","year":"1973","unstructured":"Lambert JD (1973) Computational methods in ordinary differential equations. Wiley, New York"},{"key":"93_CR17","first-page":"19","volume-title":"Gladwell I","author":"JD Lambert","year":"1980","unstructured":"Lambert JD (1980) Computation techniques for ordinary differential equations. In: Sayers DK (ed) Gladwell I. Academic, London, pp 19\u201346"},{"key":"93_CR18","first-page":"128","volume":"5","author":"M Lotkin","year":"1951","unstructured":"Lotkin M (1951) On the accuracy of RK methods. MYAC 5:128\u2013132","journal-title":"MYAC"},{"key":"93_CR19","doi-asserted-by":"crossref","first-page":"1756","DOI":"10.1126\/science.1077635","volume":"298","author":"L Mayer","year":"2002","unstructured":"Mayer L, Quinn T, Wadsley J, Stadel J (2002) Formation of giant planets by fragmentation of protoplanetary disks. Science 298:1756\u20131759","journal-title":"Science"},{"key":"93_CR20","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.1086\/421288","volume":"609","author":"L Mayer","year":"2004","unstructured":"Mayer L, Quinn T, Wadsley J, Stadel J (2004) The evolution of gravitationally unstable protoplanetary disks: Fragmentation and possible giant planet formation. Astrophys J 609:1045\u20131064","journal-title":"Astrophys J"},{"key":"93_CR21","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1086\/308238","volume":"529","author":"AF Nelson","year":"2000","unstructured":"Nelson AF, Benz W, Ruzmaikina TV (2000) Dynamics of circumstellar disks. II. Heating and cooling. Astrophys J 529:357\u2013390","journal-title":"Astrophys J"},{"key":"93_CR22","doi-asserted-by":"crossref","first-page":"2801","DOI":"10.1142\/S0217751X08039633","volume":"23","author":"GC Paul","year":"2008","unstructured":"Paul GC, Pramanik JN, Bhattacharjee SK (2008) Structure of initial protoplanets. Int J Mod Phys A 23:2801\u20132808","journal-title":"Int J Mod Phys A"},{"key":"93_CR23","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1006\/icar.1996.0190","volume":"124","author":"JB Pollack","year":"1996","unstructured":"Pollack JB, Hubickyj O, Bodenheimer P, Lissauer JJ, Podolak M, Greenzweig Y (1996) Formation of the giant planets by concurrent accretion of solids and gas. Icarus 124:62\u201385","journal-title":"Icarus"},{"key":"93_CR24","doi-asserted-by":"crossref","unstructured":"Ponalagusamy R, Senthilkumar S (2009) A New Fourth Order Embedded RKAHeM(4,4) Method with Error Control for Multilayer Raster Cellular Neural Network. SIVP 3:1\u201311","DOI":"10.1007\/s11760-007-0041-4"},{"key":"93_CR25","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1504\/IJAIP.2011.038115","volume":"3","author":"P Ponalagusamy","year":"2011","unstructured":"Ponalagusamy R, Senthilkumar S (2011) Investigation on Time-Multiplexing Cellular Neural Network Simulation by RKAHeM(4,4) Technique. IJAIP 3:43\u201366","journal-title":"IJAIP"},{"key":"93_CR26","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1090\/S0025-5718-1962-0150954-0","volume":"16","author":"RH Ralston","year":"1957","unstructured":"Ralston RH (1957) Runge\u2013Kutta methods with minimum error bonds. Math Comput 16:431\u2013437","journal-title":"Math Comput"},{"key":"93_CR27","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1046\/j.1365-8711.2003.06253.x","volume":"339","author":"WKM Rice","year":"2003","unstructured":"Rice WKM, Armitage PJ, Bate MR, Bonnell IA (2003) The effect of cooling on the global stability of self-gravitating protoplanetary discs. MNRAS 339:1025\u20131030","journal-title":"MNRAS"},{"key":"93_CR28","unstructured":"Senthilkumar S (2009) New Embedded Runge\u2013Kutta Fourth order Four Stage Algorithms for Raster and Time-Multiplexing Cellular Neural Networks Simulation, Ph.D. Thesis, Department of Mathematics, National Institute of Technology [REC], Tiruchirappalli,Tamilnadu, INDIA"},{"key":"93_CR29","volume-title":"Computer solution of ordinary differential equations-the initial value problem","author":"LF Shampine","year":"1975","unstructured":"Shampine LF, Gordon MK (1975) Computer solution of ordinary differential equations-the initial value problem. W.H. Freeman & Co, San Francisco"},{"key":"93_CR30","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1080\/00207169908804817","volume":"71","author":"AR Yaakub","year":"1999","unstructured":"Yaakub AR, Evans DJ (1999) A fourth order Runge\u2013Kutta RK(4, 4)method with error control. Int J Comput Math 71:383\u2013411","journal-title":"Int J Comput Math"}],"container-title":["Earth Science Informatics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12145-011-0093-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12145-011-0093-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12145-011-0093-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,25]],"date-time":"2019-06-25T00:50:50Z","timestamp":1561423850000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12145-011-0093-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,3]]}},"alternative-id":["93"],"URL":"https:\/\/doi.org\/10.1007\/s12145-011-0093-4","relation":{},"ISSN":["1865-0473","1865-0481"],"issn-type":[{"value":"1865-0473","type":"print"},{"value":"1865-0481","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3]]}}}