{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T15:46:18Z","timestamp":1760888778199,"version":"3.41.0"},"reference-count":27,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2013,2,1]],"date-time":"2013-02-01T00:00:00Z","timestamp":1359676800000},"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":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2013,2]]},"abstract":"<jats:p>In this article we describe the code bvptwp.m, a MATLAB code for the solution of two point boundary value problems. This code is based on the well-known Fortran codes, twpbvp.f, twpbvpl.f and acdc.f, that employ a mesh selection strategy based on the estimation of the local error, and on revisions of these codes, called twpbvpc.f, twpbvplc.f and acdcc.f, that employ a mesh selection strategy based on the estimation of the local error and the estimation of two parameters which characterize the conditioning of the problem. The codes twpbvp.f\/tpbvpc.f use a deferred correction scheme based on Mono-Implicit Runge-Kutta methods (MIRK); the other codes use a deferred correction scheme based on Lobatto formulas. The acdc.f\/acdcc.f codes implement an automatic continuation strategy. The performance and features of the new solver are checked by performing some numerical tests to show that the new code is robust and able to solve very difficult singularly perturbed problems. The results obtained show that bvptwp.m is often able to solve problems requiring stringent accuracies and problems with very sharp changes in the solution. This code, coupled with the existing boundary value codes such as bvp4c.m, makes the MATLAB BVP section an extremely powerful one for a very wide range of problems.<\/jats:p>","DOI":"10.1145\/2427023.2427032","type":"journal-article","created":{"date-parts":[[2013,2,22]],"date-time":"2013-02-22T19:25:04Z","timestamp":1361561104000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":19,"title":["Algorithm 927"],"prefix":"10.1145","volume":"39","author":[{"given":"J. R.","family":"Cash","sequence":"first","affiliation":[{"name":"Imperial College, UK"}]},{"given":"D.","family":"Hollevoet","sequence":"additional","affiliation":[{"name":"Universiteit Gent, Belgium"}]},{"given":"F.","family":"Mazzia","sequence":"additional","affiliation":[{"name":"Universit\u00e0 di Bari, Italy"}]},{"given":"A. M.","family":"Nagy","sequence":"additional","affiliation":[{"name":"Universit\u00e0 di Bari, Italy"}]}],"member":"320","published-online":{"date-parts":[[2013,2]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/355945.355950"},{"key":"e_1_2_2_2_1","volume-title":"Numerical Solution of Boundary Value Problems for Ordinary Differential Equations. Classics in Applied Mathematics Series","volume":"13","author":"Ascher U. M.","year":"1988","unstructured":"Ascher , U. M. , Mattheij , R. M. M. , and Russell , R. D . 1995 . Numerical Solution of Boundary Value Problems for Ordinary Differential Equations. Classics in Applied Mathematics Series , vol. 13 , SIAM, Philadelphia, PA. (Corrected reprint of the 1988 original.) Ascher, U. M., Mattheij, R. M. M., and Russell, R. D. 1995. Numerical Solution of Boundary Value Problems for Ordinary Differential Equations. Classics in Applied Mathematics Series, vol. 13, SIAM, Philadelphia, PA. (Corrected reprint of the 1988 original.)"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(98)80009-6"},{"key":"e_1_2_2_4_1","doi-asserted-by":"crossref","unstructured":"Brugnano L. Mazzia F. and Trigiante D. 2011. Fifty years of stiffness. In Recent Advances in Computational and Applied Mathematics Springer 1--22.  Brugnano L. Mazzia F. and Trigiante D. 2011. Fifty years of stiffness. In Recent Advances in Computational and Applied Mathematics Springer 1--22.","DOI":"10.1007\/978-90-481-9981-5_1"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1137\/0725049"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.5555\/1150674.1716594"},{"key":"e_1_2_2_7_1","unstructured":"Cash J. R. and Mazzia F. 2006a. Algorithms for the solution of two-point boundary value problems. http:\/\/www.ma.ic.ac.uk\/~jcash\/BVP_software\/twpbvp.php.  Cash J. R. and Mazzia F. 2006a. Algorithms for the solution of two-point boundary value problems. http:\/\/www.ma.ic.ac.uk\/~jcash\/BVP_software\/twpbvp.php."},{"key":"e_1_2_2_8_1","first-page":"81","article-title":"Hybrid mesh selection algorithms based on conditioning for two-point boundary value problems","volume":"1","author":"Cash J. R.","year":"2006","unstructured":"Cash , J. R. and Mazzia , F. 2006 b. Hybrid mesh selection algorithms based on conditioning for two-point boundary value problems . J. Numer. Anal. Ind. Appl. Math. 1 , 1, 81 -- 90 . Cash, J. R. and Mazzia, F. 2006b. Hybrid mesh selection algorithms based on conditioning for two-point boundary value problems. J. Numer. Anal. Ind. Appl. Math. 1, 1, 81--90.","journal-title":"J. Numer. Anal. Ind. Appl. Math."},{"key":"e_1_2_2_9_1","first-page":"347","article-title":"Conditioning and hybrid mesh selection algorithms for two point boundary value problems","volume":"10","author":"Cash J. R.","year":"2009","unstructured":"Cash , J. R. and Mazzia , F. 2009 . Conditioning and hybrid mesh selection algorithms for two point boundary value problems . Scalable Comput. Pract. Exper. 10 , 4, 347 -- 361 . Cash, J. R. and Mazzia, F. 2009. Conditioning and hybrid mesh selection algorithms for two point boundary value problems. Scalable Comput. Pract. Exper. 10, 4, 347--361.","journal-title":"Scalable Comput. Pract. 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Fox, L. 1957. The Numerical Solution of Two-Point Boundary Problems in Ordinary Differential Equations. Oxford University Press, New York."},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/502800.502801"},{"key":"e_1_2_2_20_1","first-page":"1","article-title":"A BVP solver that controls residual and error","volume":"3","author":"Kierzenka J.","year":"2008","unstructured":"Kierzenka , J. and Shampine , L. F. 2008 . A BVP solver that controls residual and error . J. Numer. Anal. Ind. Appl. Math. 3 , 1 -- 2 , 27--41. Kierzenka, J. and Shampine, L. F. 2008. A BVP solver that controls residual and error. J. Numer. Anal. Ind. Appl. Math. 3, 1--2, 27--41.","journal-title":"J. Numer. Anal. Ind. Appl. Math."},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01933642"},{"key":"e_1_2_2_22_1","volume-title":"Matlab release","author":"Mathworks T.","year":"2012","unstructured":"Mathworks , T. 2012. Matlab release 2012 a. http:\/\/www.mathworks.com\/. 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