{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:42:03Z","timestamp":1750308123579,"version":"3.41.0"},"reference-count":13,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[1981,8,1]],"date-time":"1981-08-01T00:00:00Z","timestamp":365472000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGSAM Bull."],"published-print":{"date-parts":[[1981,8]]},"abstract":"<jats:p>This paper describes a symbolic ordinary differential equation solver written as a package for the muMATH computer algebra system. The novel features of this solver are:1. Whereas previous ODE solvers generally require the equation to be quasi-linear and generally yield only implicit results, this new solver is highly integrated with an algebraic equation solver before, during and after solution. In fact, the same function named SOLVE is used for both algebraic and differential equations.2. By not insisting upon quasi-linear input, it is also practical to incorporate in the same solver methods for quasi-linear equations and a generalized version of Clairaut's equation, including singular envelope solutions. To my knowledge, previous ODE solvers have not treated even the ordinary Clairaut's equation, even using a separate solver.3. Since integration constants introduced at intermediate stages can become deeply embedded in a final explicit solution, the new solver automatically replaces subexpressions containing only an integration constant and numerical constants with a new constant, in order to greatly simplify the appearance of results, with no loss of generality.4. Whereas previous ODE solvers are generally restricted to first or second order (or to linear equations with constant coefficients) the new solver attempts to solve equations of any order, even if they are nonlinear and\/or have variable coefficients.5. When the new solver is unable to obtain a closed-form solution, Picard iteration or a Taylor-series method is automatically employed so as to obtain a symbolic truncated series solution.muMATH does not yet provide the algebraic operations necessary to support the recently-discovered ODE decision procedures. Consequently the methods used to solve quasi-linear first and second order equations are essentially the same as those employed by other solvers of the pre-decision-procedure era.<\/jats:p>","DOI":"10.1145\/1089263.1089264","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"9-14","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["A novel symbolic ordinary differential equation solver"],"prefix":"10.1145","volume":"15","author":[{"given":"Woon Cheung","family":"Chan","sequence":"first","affiliation":[{"name":"University of Hawaii at Manoa"}]}],"member":"320","published-online":{"date-parts":[[1981,8]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"The muMATH\/muSIMP-80 Symbolic Mathematics System Reference Manual Microsoft 10800 NE Eight Suite 819 Bellevue Washington 98004.  The muMATH\/muSIMP-80 Symbolic Mathematics System Reference Manual Microsoft 10800 NE Eight Suite 819 Bellevue Washington 98004."},{"key":"e_1_2_1_2_1","first-page":"327","volume-title":"MIT Laboratory for Computer Science","author":"Fateman R. J.","year":"1977","unstructured":"Fateman , R. J. , \" Some Comments of Series Solution ,\" Proceedings of the 1977 MACSYMA's User's Conference , MIT Laboratory for Computer Science , 1977 , p. 327 -- 346 . Fateman, R. J., \"Some Comments of Series Solution,\" Proceedings of the 1977 MACSYMA's User's Conference, MIT Laboratory for Computer Science, 1977, p. 327--346."},{"key":"e_1_2_1_3_1","first-page":"1","volume-title":"MIT Laboratory for Computer Science","author":"Golden J. P.","year":"1977","unstructured":"Golden , J. P. , \"MACSYM A's Symbolic Ordinary Differential Equation Solver ,\" Proceedings of the 1977 MACSYM's User's Conference , MIT Laboratory for Computer Science , 1977 , p. 1 -- 10 . Golden, J. P., \"MACSYMA's Symbolic Ordinary Differential Equation Solver,\" Proceedings of the 1977 MACSYM's User's Conference, MIT Laboratory for Computer Science, 1977, p. 1--10."},{"key":"e_1_2_1_4_1","first-page":"11210","author":"Kovacic J. J.","year":"1979","unstructured":"Kovacic , J. J. , \" An Algorithm for Solving Second Order Linear Homogeneous Differential Equations ,\" Brooklyn College of the City University of New York, Brooklyn , NY 11210 , 1979 . Kovacic, J. J., \"An Algorithm for Solving Second Order Linear Homogeneous Differential Equations,\" Brooklyn College of the City University of New York, Brooklyn, NY 11210, 1979.","journal-title":"NY"},{"key":"e_1_2_1_5_1","first-page":"347","volume-title":"MIT Laboratory for Computer Science","author":"Lafferty E. L.","year":"1977","unstructured":"Lafferty , E. L. , \" Power Series Solution of Ordinary Equations ,\" Proceedings of the 1977 MACSYMA's User's Conference , MIT Laboratory for Computer Science , 1977 , p. 347 -- 360 . Lafferty, E. L., \"Power Series Solution of Ordinary Equations,\" Proceedings of the 1977 MACSYMA's User's Conference, MIT Laboratory for Computer Science, 1977, p. 347--360."},{"key":"e_1_2_1_6_1","first-page":"397","volume-title":"Proceedings of 1979 MACSYMA's User's Conference, MIT Laboratory for Computer Science","author":"Lafferty E. L.","year":"1979","unstructured":"Lafferty , E. L. , \" Differential Operator Factorization and Riccati Equation ,\" Proceedings of 1979 MACSYMA's User's Conference, MIT Laboratory for Computer Science , 1979 , p. 397 -- 407 . Lafferty, E. L., \"Differential Operator Factorization and Riccati Equation,\" Proceedings of 1979 MACSYMA's User's Conference, MIT Laboratory for Computer Science, 1979, p. 397--407."},{"key":"e_1_2_1_7_1","volume-title":"DIFFERENTIAL EQUATIONS FOR ENGINEERS AND SCIENTISTS","author":"Lambe C. G.","year":"1956","unstructured":"Lambe , C. G. and Tranter , C. J. , DIFFERENTIAL EQUATIONS FOR ENGINEERS AND SCIENTISTS , English University Press , 1956 . Lambe, C. G. and Tranter, C. J., DIFFERENTIAL EQUATIONS FOR ENGINEERS AND SCIENTISTS, English University Press, 1956."},{"key":"e_1_2_1_8_1","volume-title":"MIT","author":"Moses J., SYMBOLIC INTEGRATION","year":"1967","unstructured":"Moses , J., SYMBOLIC INTEGRATION , Report MAC TR-47 , MIT , 1967 . Moses, J., SYMBOLIC INTEGRATION, Report MAC TR-47, MIT, 1967."},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/362637.362651"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/800205.806329"},{"key":"e_1_2_1_11_1","first-page":"164","author":"Schmidt P.","year":"1979","unstructured":"Schmidt . P. , \" Substitution Methods for the Automatic Symbolic Solution of Differential Equations of First Order and First Degree ,\" EUROSAM '79 , Springer-Verlag , 1979 , p. 164 -- 176 . Schmidt. P., \"Substitution Methods for the Automatic Symbolic Solution of Differential Equations of First Order and First Degree,\" EUROSAM '79, Springer-Verlag, 1979, p. 164--176.","journal-title":"Springer-Verlag"},{"key":"e_1_2_1_12_1","volume-title":"DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES","author":"Simmons G. F.","year":"1972","unstructured":"Simmons , G. F. , DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES , McGraw-Hill , 1972 . Simmons, G. F., DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES, McGraw-Hill, 1972."},{"key":"e_1_2_1_13_1","volume-title":"APPLIED DIFFERENTIAL EQUATIONS","author":"Spiegel M. R.","year":"1958","unstructured":"Spiegel , M. R. , APPLIED DIFFERENTIAL EQUATIONS , Prentice-Hall, Inc. , 1958 . Spiegel, M. R., APPLIED DIFFERENTIAL EQUATIONS, Prentice-Hall, Inc., 1958."}],"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1089263.1089264","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1089263.1089264","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T16:08:22Z","timestamp":1750262902000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1089263.1089264"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1981,8]]},"references-count":13,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1981,8]]}},"alternative-id":["10.1145\/1089263.1089264"],"URL":"https:\/\/doi.org\/10.1145\/1089263.1089264","relation":{},"ISSN":["0163-5824"],"issn-type":[{"type":"print","value":"0163-5824"}],"subject":[],"published":{"date-parts":[[1981,8]]},"assertion":[{"value":"1981-08-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}