{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T16:38:56Z","timestamp":1648571936449},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2013,9,28]],"date-time":"2013-09-28T00:00:00Z","timestamp":1380326400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2014,9]]},"DOI":"10.1007\/s11075-013-9773-0","type":"journal-article","created":{"date-parts":[[2013,9,27]],"date-time":"2013-09-27T01:30:39Z","timestamp":1380245439000},"page":"49-57","source":"Crossref","is-referenced-by-count":0,"title":["Laplace transform for the solution of higher order deformation equations arising in the homotopy analysis method"],"prefix":"10.1007","volume":"67","author":[{"given":"Songxin","family":"Liang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junchi","family":"Ma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,9,28]]},"reference":[{"key":"9773_CR1","doi-asserted-by":"crossref","DOI":"10.1201\/9780203491164","volume-title":"Beyond Perturbation\u2014Introduction to the Homotopy Analysis Method","author":"SJ Liao","year":"2003","unstructured":"Liao, S.J.: Beyond Perturbation\u2014Introduction to the Homotopy Analysis Method. Chapman & Hall\/CRC, Boca Raton (2003)"},{"key":"9773_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-25132-0","volume-title":"Homotopy Analysis Method in Nonlinear Differential Equations","author":"SJ Liao","year":"2012","unstructured":"Liao, S.J.: Homotopy Analysis Method in Nonlinear Differential Equations. Springer & Higher Education Press, Heidelberg (2012)"},{"key":"9773_CR3","doi-asserted-by":"crossref","first-page":"4057","DOI":"10.1016\/j.cnsns.2009.02.016","volume":"14","author":"SX Liang","year":"2009","unstructured":"Liang, S.X., Jeffrey, D.J.: Comparison of homotopy analysis method and homotopy perturbation method through an evolution equation. Commun. Nonlinear Sci. 14, 4057\u20134064 (2009)","journal-title":"Commun. Nonlinear Sci."},{"key":"9773_CR4","doi-asserted-by":"crossref","first-page":"3140","DOI":"10.1016\/j.cnsns.2010.11.018","volume":"16","author":"S Abbasbandy","year":"2011","unstructured":"Abbasbandy, S., Hayat, T.: On series solution for unsteady boundary layer equations in a special third grade fluid. Commun. Nonlinear Sci. 16, 3140\u20133146 (2011)","journal-title":"Commun. Nonlinear Sci."},{"key":"9773_CR5","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1016\/j.nonrwa.2012.07.015","volume":"14","author":"F Guerrero","year":"2013","unstructured":"Guerrero, F., Santonja, F.J., Villanueva, R.J.: Solving a model for the evolution of smoking habit in Spain with homotopy analysis method. Nonlinear Anal.-Real 14, 549\u2013558 (2013)","journal-title":"Nonlinear Anal.-Real"},{"key":"9773_CR6","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/s11075-010-9375-z","volume":"56","author":"SX Liang","year":"2011","unstructured":"Liang, S.X., Jeffrey, D.J.: An analytical approach for solving nonlinear boundary value problems in finite domains. Numer. Algorithms 56, 93\u2013106 (2011)","journal-title":"Numer. Algorithms"},{"key":"9773_CR7","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1007\/s11075-012-9548-z","volume":"61","author":"H Vosoughi","year":"2012","unstructured":"Vosoughi, H., Shivanian, E., Abbasbandy, S.: Unique and multiple PHAM series solutions of a class of nonlinear reactive transport model. Numer. Algorithms 61, 515\u2013524 (2012)","journal-title":"Numer. Algorithms"},{"key":"9773_CR8","doi-asserted-by":"crossref","first-page":"2293","DOI":"10.1016\/j.cnsns.2009.09.019","volume":"15","author":"SS Motsa","year":"2010","unstructured":"Motsa, S.S., Sibanda, P., Shateyi, S.: A new spectral-homotopy analysis method for solving a nonlinear second order BVP. Commun. Nonlinear Sci. 15, 2293\u20132302 (2010)","journal-title":"Commun. Nonlinear Sci."},{"key":"9773_CR9","volume-title":"Operational Mathematics","author":"RV Churchill","year":"1972","unstructured":"Churchill, R.V.: Operational Mathematics, 3rd edn. McGraw-Hill, New York (1972)","edition":"3"},{"key":"9773_CR10","volume-title":"Elementary Differential Equations","author":"CH Edwards","year":"2007","unstructured":"Edwards, C.H., Penney, D.E.: Elementary Differential Equations, 6th edn. Pearson Prentice Hall, New Jersey (2007)","edition":"6"},{"key":"9773_CR11","doi-asserted-by":"crossref","first-page":"1265","DOI":"10.1016\/j.nonrwa.2012.09.005","volume":"14","author":"BM Vaganan","year":"2013","unstructured":"Vaganan, B.M., Priya, T.S.: Exact analytic, regular perturbation and numerical solutions of symmetry reductions of a (2+1)-dimensional KdV-Burgers equation. Nonlinear Anal.-Real 14, 1265\u20131275 (2013)","journal-title":"Nonlinear Anal.-Real"},{"key":"9773_CR12","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.jmaa.2004.12.014","volume":"309","author":"PE Hydon","year":"2005","unstructured":"Hydon, P.E.: Symmetry analysis of initial-value problems. J. Math. Anal. Appl. 309, 103\u2013116 (2005)","journal-title":"J. Math. Anal. Appl."},{"key":"9773_CR13","doi-asserted-by":"crossref","first-page":"4078","DOI":"10.1016\/j.cnsns.2009.03.008","volume":"14","author":"RA Gorder Van","year":"2009","unstructured":"Van Gorder, R.A., Vajravelu, K.: On the selection of auxiliary functions, operators, and convergence control parameters in the application of the Homotopy Analysis Method to nonlinear differential equations: a general approach. Commun. Nonlinear Sci. 14, 4078\u20134089 (2009)","journal-title":"Commun. Nonlinear Sci."},{"key":"9773_CR14","doi-asserted-by":"crossref","first-page":"1163","DOI":"10.1016\/j.cnsns.2011.08.003","volume":"17","author":"M Ghoreishi","year":"2012","unstructured":"Ghoreishi, M., Ismail, A.I.B.M., Alomari, A.K., Bataineh, A.S.: The comparison between Homotopy Analysis Method and Optimal Homotopy Asymptotic Method for nonlinear age structured population models. Commun. Nonlinear Sci. 17, 1163\u20131177 (2012)","journal-title":"Commun. Nonlinear Sci."},{"key":"9773_CR15","doi-asserted-by":"crossref","first-page":"4268","DOI":"10.1016\/j.cnsns.2011.03.031","volume":"16","author":"S Abbasbandy","year":"2011","unstructured":"Abbasbandy, S., Shivanian, E., Vajravelu, K.: Mathematical properties of h-curve in the frame work of the homotopy analysis method. Commun. Nonlinear Sci. 16, 4268\u20134275 (2011)","journal-title":"Commun. Nonlinear Sci."},{"key":"9773_CR16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ijnonlinmec.2012.01.004","volume":"47","author":"RA Gorder Van","year":"2012","unstructured":"Van Gorder, R.A.: Analytical method for the construction of solutions to the Foppl-von Karman equations governing deflections of a thin flat plate. Int. J. Nonlin. Mech. 47, 1\u20136 (2012)","journal-title":"Int. J. Nonlin. Mech."},{"key":"9773_CR17","doi-asserted-by":"crossref","first-page":"1233","DOI":"10.1016\/j.cnsns.2011.07.036","volume":"17","author":"RA Gorder Van","year":"2012","unstructured":"Van Gorder, R.A.: Gaussian waves in the Fitzhugh-Nagumo equation demonstrate one role of the auxiliary function H(x) in the homotopy analysis method. Commun. Nonlinear Sci. 17, 1233\u20131240 (2012)","journal-title":"Commun. Nonlinear Sci."},{"key":"9773_CR18","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1007\/s11075-012-9554-1","volume":"61","author":"R.A Gorder Van","year":"2012","unstructured":"Van Gorder, R.A.: Control of error in the homotopy analysis of semi-linear elliptic boundary value problems. Numer. Algorithms 61, 613\u2013629 (2012)","journal-title":"Numer. Algorithms"},{"key":"9773_CR19","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/s11075-012-9587-5","volume":"62","author":"T Fan","year":"2013","unstructured":"Fan, T., You, X.C.: Optimal homotopy analysis method for nonlinear differential equations in the boundary layer. Numer. Algorithms 62, 337\u2013354 (2013)","journal-title":"Numer. Algorithms"},{"key":"9773_CR20","doi-asserted-by":"crossref","first-page":"2003","DOI":"10.1016\/j.cnsns.2009.09.002","volume":"15","author":"SJ Liao","year":"2010","unstructured":"Liao, S.J.: An optimal homotopy-analysis approach for strongly nonlinear differential equations. Commun. Nonlinear Sci. 15, 2003\u20132016 (2010)","journal-title":"Commun. Nonlinear Sci."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-013-9773-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-013-9773-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-013-9773-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T01:08:22Z","timestamp":1559351302000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-013-9773-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9,28]]},"references-count":20,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,9]]}},"alternative-id":["9773"],"URL":"https:\/\/doi.org\/10.1007\/s11075-013-9773-0","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,9,28]]}}}