{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,21]],"date-time":"2024-09-21T11:58:21Z","timestamp":1726919901416},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,4,3]],"date-time":"2019-04-03T00:00:00Z","timestamp":1554249600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2020,4]]},"DOI":"10.1007\/s00366-019-00727-y","type":"journal-article","created":{"date-parts":[[2019,4,4]],"date-time":"2019-04-04T03:19:01Z","timestamp":1554347941000},"page":"725-739","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Solving two-dimensional integral equations of the second kind on non-rectangular domains with error estimate"],"prefix":"10.1007","volume":"36","author":[{"given":"Kourosh","family":"Parand","sequence":"first","affiliation":[]},{"given":"Hafez","family":"Yari","sequence":"additional","affiliation":[]},{"given":"Mehdi","family":"Delkhosh","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,4,3]]},"reference":[{"key":"727_CR1","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/0021-8928(91)90041-R","volume":"55","author":"BI Smetanin","year":"1991","unstructured":"Smetanin BI (1991) On an integral equation for axially-symmetric problems in the case of an elastic body containing an inclusion. J Appl Math Mech 55:371\u2013375","journal-title":"J Appl Math Mech"},{"key":"727_CR2","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1016\/0021-8928(85)90016-4","volume":"49","author":"AV Manzhirov","year":"1985","unstructured":"Manzhirov AV (1985) On a method of solving two-dimensional integral equations of axisymmetric contact problems for bodies with complex rheology. J Appl Math Mech 49:777\u2013782","journal-title":"J Appl Math Mech"},{"key":"727_CR3","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1090\/S0002-9904-1964-11209-X","volume":"70","author":"J Radlow","year":"1964","unstructured":"Radlow J (1964) A two-dimensional singular integral equation of diffraction theory. Bull Am Math Soc 70:596\u2013599","journal-title":"Bull Am Math Soc"},{"key":"727_CR4","doi-asserted-by":"crossref","first-page":"931","DOI":"10.1137\/0153046","volume":"53","author":"J Boersma","year":"1993","unstructured":"Boersma J, Danick E (1993) On the solution of an integral equation arising in potential problems for circular and elliptic disks. SIAM J Appl Math 53:931\u2013941","journal-title":"SIAM J Appl Math"},{"key":"727_CR5","doi-asserted-by":"crossref","first-page":"1215","DOI":"10.1063\/1.1665723","volume":"12","author":"P Wolfe","year":"1971","unstructured":"Wolfe P (1971) Eigenfunctions of the integral equation for the potential of the charged disk. J Math Phys 12:1215\u20131218","journal-title":"J Math Phys"},{"key":"727_CR6","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/0021-8928(89)90138-X","volume":"53","author":"EV Kovalenko","year":"1989","unstructured":"Kovalenko EV (1989) Some approximate methods of solving integral equations of mixed problems. J Appl Math Mech 53:85\u201392","journal-title":"J Appl Math Mech"},{"key":"727_CR7","first-page":"641","volume":"103","author":"EV Kovalenco","year":"1999","unstructured":"Kovalenco EV (1999) Some approximate methods for solving integral equations of mixed problems. Probl Math Appl 103:641\u2013655","journal-title":"Probl Math Appl"},{"key":"727_CR8","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/0021-8928(91)90041-R","volume":"55","author":"BJ Semetanian","year":"1991","unstructured":"Semetanian BJ (1991) On an integral equation for axially symmetric problem in the case of an elastic body containing an inclusion. J Appl Math Mech 55:371\u2013375","journal-title":"J Appl Math Mech"},{"key":"727_CR9","doi-asserted-by":"crossref","first-page":"3515","DOI":"10.1063\/1.864112","volume":"26","author":"R Farengo","year":"1983","unstructured":"Farengo R, Lee YC, Guzdar PN (1983) An electromagnetic integral equation: application to microtearing modes. Phys Fluids 26:3515\u20133523","journal-title":"Phys Fluids"},{"key":"727_CR10","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1080\/00268976.2016.1234079","volume":"115","author":"M Borowko","year":"2017","unstructured":"Borowko M, Rzysko W, Sokoowski S, Staszewski T (2017) Integral equations theory for two-dimensional systems involving nanoparticles. Mol Phys 115:1065\u20131073","journal-title":"Mol Phys"},{"key":"727_CR11","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/0022-0728(92)80002-L","volume":"323","author":"MV Mirkin","year":"1992","unstructured":"Mirkin MV, Bard AJ (1992) Multidimensional integral equations: a new approach to solving microelectrode diffusion problems: part 2. Applications to microband electrodes and the scanning electrochemical microscope. J Electroanal Chem 323:29\u201351","journal-title":"J Electroanal Chem"},{"key":"727_CR12","doi-asserted-by":"crossref","first-page":"393","DOI":"10.2528\/PIER08012502","volume":"81","author":"S Hatamzadeh-Varmazyar","year":"2008","unstructured":"Hatamzadeh-Varmazyar S, Naser-Moghadasi M, Babolian E, Masouri Z (2008) Numerical approach to survey the problem of electromagnetic scattering from resistive based on using a set of orthogonal basis functions. Prog Electromagn Res 81:393\u2013412","journal-title":"Prog Electromagn Res"},{"key":"727_CR13","doi-asserted-by":"crossref","first-page":"113","DOI":"10.2528\/PIER07041506","volume":"74","author":"MS Tong","year":"2007","unstructured":"Tong MS (2007) A stable integral equation solver for electromagnetic scattering by large scatters with concave surface. Prog Electromagn Res 74:113\u2013130","journal-title":"Prog Electromagn Res"},{"key":"727_CR14","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/s00780-005-0153-z","volume":"9","author":"E Voltchkova","year":"2005","unstructured":"Voltchkova E (2005) Integro-differential equations for option prices in exponential Levy models. Finance Stoch 9:299\u2013325","journal-title":"Finance Stoch"},{"key":"727_CR15","first-page":"4977","volume":"219","author":"R Ansari","year":"2013","unstructured":"Ansari R, Hosseini K, Darvizeh A, Daneshian B (2013) A sixth-order compact finite difference method for non-classical vibration analysis of nanobeams including surface stress effects. Appl Math Comput 219:4977\u20134991","journal-title":"Appl Math Comput"},{"key":"727_CR16","doi-asserted-by":"crossref","first-page":"2577","DOI":"10.1016\/j.mcm.2011.06.030","volume":"54","author":"R Ansari","year":"2011","unstructured":"Ansari R, Gholami R, Hosseini K, Sahmani S (2011) A sixth-order compact finite difference method for vibrational analysis of nanobeams embedded in an elastic medium based on nonlocal beam theory. Math Comput Model 54:2577\u20132586","journal-title":"Math Comput Model"},{"key":"727_CR17","first-page":"195","volume":"127","author":"S Yalcinbas","year":"2002","unstructured":"Yalcinbas S (2002) Taylor polynomial solutions of nonlinear Volterra\u2013Fredholm integral equations. Appl Math Comput 127:195\u2013206","journal-title":"Appl Math Comput"},{"key":"727_CR18","first-page":"291","volume":"112","author":"S Yalcinbas","year":"2000","unstructured":"Yalcinbas S, Sezer M (2000) The approximate solution of high-order linear Volterra\u2013Fredholm integro-differential equations in terms of Taylor polynomials. Appl Math Comput 112:291\u2013308","journal-title":"Appl Math Comput"},{"key":"727_CR19","first-page":"1418","volume":"167","author":"S Shahmorad","year":"2005","unstructured":"Shahmorad S (2005) Numerical solution of the general form linear Fredholm\u2013Volterra integro-differential equations by the Tau method with an error estimation. Appl Math Comput 167:1418\u20131429","journal-title":"Appl Math Comput"},{"key":"727_CR20","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.1007\/s13370-014-0283-6","volume":"26","author":"F Hosseini Shekarabi","year":"2015","unstructured":"Shekarabi F Hosseini, Maleknejad K, Ezzati R (2015) Application of two-dimensional Bernstein polynomials for solving mixed Volterra\u2013Fredholm integral equations. Afr Mat 26:1237\u20131251","journal-title":"Afr Mat"},{"key":"727_CR21","doi-asserted-by":"crossref","first-page":"1164","DOI":"10.1016\/j.cnsns.2010.05.029","volume":"16","author":"E Babolian","year":"2011","unstructured":"Babolian E, Bazm S, Lima P (2011) Numerical solution of nonlinear two-dimensional integral equations using rationalized Haar functions. Commun Nonlinear Sci Numer Simul 16:1164\u20131175","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"727_CR22","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1515\/ijnsns-2016-0160","volume":"18","author":"MA Abdelkawy","year":"2017","unstructured":"Abdelkawy MA, Amin AZM, Bhrawy AH, Machado JA, Lopes AM (2017) Jacobi collocation approximation for solving multi-dimensional Volterra integral equations. Int J Nonlinear Sci Numer Simul 18:411\u2013426","journal-title":"Int J Nonlinear Sci Numer Simul"},{"key":"727_CR23","first-page":"759","volume":"265","author":"F Mirzaee","year":"2015","unstructured":"Mirzaee F, Hadadiyan E (2015) Applying the modified block-pulse functions to solve the three-dimensional Volterra\u2013Fredholm integral equations. Appl Math Comput 265:759\u2013767","journal-title":"Appl Math Comput"},{"key":"727_CR24","first-page":"179","volume":"20","author":"Y Ordokhani","year":"2015","unstructured":"Ordokhani Y, Moosavi S (2015) Numerical solution of three-dimensional Volterra\u2013Fredholm integral equations of the first and second kinds based on Bernstein\u2019s approximation. Int J Nonlinear Sci 20:179\u2013192","journal-title":"Int J Nonlinear Sci"},{"key":"727_CR25","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1002\/cnm.1166","volume":"26","author":"M Dehghan","year":"2010","unstructured":"Dehghan M, Shakeri F (2010) Solution of parabolic integro-differential equations arising in heat conduction in materials with memory via He\u2019s variational iteration technique. Int J Numer Methods Biomed Eng 26:705\u2013715","journal-title":"Int J Numer Methods Biomed Eng"},{"key":"727_CR26","doi-asserted-by":"crossref","first-page":"752","DOI":"10.1515\/zna-2008-1202","volume":"63","author":"A Saadatmandia","year":"2008","unstructured":"Saadatmandia A, Dehghan M (2008) A collocation method for solving Abel\u2019s integral equations of first and second kinds. Z Naturforsch 63:752\u2013756","journal-title":"Z Naturforsch"},{"key":"727_CR27","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1140\/epjp\/i2017-11467-y","volume":"132","author":"P Assari","year":"2017","unstructured":"Assari P, Dehghan M (2017) A meshless method for the numerical solution of nonlinear weakly singular integral equations using radial basis functions. Eur Phys J Plus 132:199\u2013222","journal-title":"Eur Phys J Plus"},{"key":"727_CR28","doi-asserted-by":"publisher","DOI":"10.1007\/s00366-018-0637-z","author":"P Assari","year":"2018","unstructured":"Assari P (2018) On the numerical solution of two-dimensional integral equations using a meshless local discrete Galerkin scheme with error analysis. Eng Comput. https:\/\/doi.org\/10.1007\/s00366-018-0637-z","journal-title":"Eng Comput"},{"key":"727_CR29","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.apnum.2018.05.001","volume":"131","author":"P Assari","year":"2018","unstructured":"Assari P, Dehghan M (2018) The approximate solution of nonlinear Volterra integral equations of the second kind using radial basis functions. Appl Numer Math 131:140\u2013157","journal-title":"Appl Numer Math"},{"key":"727_CR30","first-page":"236","volume":"298","author":"M Esmaeilbeigi","year":"2017","unstructured":"Esmaeilbeigi M, Mirzaee F, Moazami D (2017) A meshfree method for solving multidimensional linear Fredholm integral equations on the hypercube domains. Appl Math Comput 298:236\u2013246","journal-title":"Appl Math Comput"},{"key":"727_CR31","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1016\/j.cam.2017.01.030","volume":"319","author":"K Sadri","year":"2017","unstructured":"Sadri K, Amini A, Cheng C (2017) Low cost numerical solution for three-dimensional linear and nonlinear integral equations via three-dimensional Jacobi polynomials. J Comput Appl Math 319:493\u2013513","journal-title":"J Comput Appl Math"},{"key":"727_CR32","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2010\/138408","volume":"2010","author":"H Adibi","year":"2010","unstructured":"Adibi H, Assari P (2010) Chebyshev wavelet method for numerical solution of Fredholm integral equations of the first kind. Math Probl Eng 2010:1\u201317","journal-title":"Math Probl Eng"},{"key":"727_CR33","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/j.cam.2014.01.037","volume":"267","author":"P Assari","year":"2014","unstructured":"Assari P, Adibi H, Dehghan M (2014) A meshless discrete Galerkin (MDG) method for the numerical solution of integral equations with logarithmic kernels. J Comput Appl Math 267:160\u2013181","journal-title":"J Comput Appl Math"},{"key":"727_CR34","first-page":"21","volume":"9","author":"R Ketabchi","year":"2017","unstructured":"Ketabchi R, Mokhtari R, Babolian E (2017) A new approach for solving volterra integral equations using the reproducing kernel method. Int J Ind Math 9:21\u201326","journal-title":"Int J Ind Math"},{"key":"727_CR35","doi-asserted-by":"crossref","first-page":"1787","DOI":"10.1080\/00036811.2012.702209","volume":"92","author":"Z Mahmoodi","year":"2013","unstructured":"Mahmoodi Z, Rashidinia J, Babolian E (2013) B-spline collocation method for linear and nonlinear Fredholm and Volterra integro-differential equations. Appl Anal 92:1787\u20131802","journal-title":"Appl Anal"},{"key":"727_CR36","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511626340","volume-title":"The numerical solution of integral equations of the second kind","author":"KE Atkinson","year":"1997","unstructured":"Atkinson KE (1997) The numerical solution of integral equations of the second kind. Cambridge University Press, New York"},{"key":"727_CR37","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.apnum.2009.12.003","volume":"60","author":"D Mirzaei","year":"2010","unstructured":"Mirzaei D, Dehghan M (2010) A meshless based method for solution of integral equations. Appl Numer Math 60:245\u2013262","journal-title":"Appl Numer Math"},{"key":"727_CR38","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1007\/s11075-013-9800-1","volume":"67","author":"P Assari","year":"2012","unstructured":"Assari P, Adibi H, Dehghan M (2012) A meshless method based on the moving least squares (MLS) approximation for the numerical solution of two-dimensional nonlinear integral equations of the second kind on non-rectangular domains. Numer Algorithms 67:423\u2013455","journal-title":"Numer Algorithms"},{"key":"727_CR39","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.cam.2012.09.010","volume":"239","author":"P Assari","year":"2013","unstructured":"Assari P, Adibi H, Dehghan M (2013) A meshless method for solving nonlinear two-dimensional integral equations of the second kind on non-rectangular domains using radial basis functions with error analysis. J Comput Appl Math 239:72\u201392","journal-title":"J Comput Appl Math"},{"key":"727_CR40","doi-asserted-by":"crossref","first-page":"9269","DOI":"10.1016\/j.apm.2013.04.047","volume":"73","author":"P Assari","year":"2013","unstructured":"Assari P, Adibi H, Dehghan M (2013) A numerical method for solving linear integral equations of the second kind on the non-rectangular domains based on the meshless method. Appl Math Model 73:9269\u20139294","journal-title":"Appl Math Model"},{"key":"727_CR41","first-page":"519","volume":"69","author":"K Parand","year":"2018","unstructured":"Parand K, Latifi S, Moayeri MM, Delkhosh M (2018) Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) collocation method for solving linear and nonlinear Fokker\u2013Planck equations. Commun Math Phys 69:519\u2013531","journal-title":"Commun Math Phys"},{"key":"727_CR42","doi-asserted-by":"crossref","first-page":"33","DOI":"10.5269\/bspm.v36i4.31478","volume":"36","author":"K Parand","year":"2018","unstructured":"Parand K, Delkhosh M (2018) Systems of nonlinear Volterra integro-differential equations of arbitrary order. Bol Soc Paran Mat 36:33\u201354","journal-title":"Bol Soc Paran Mat"},{"key":"727_CR43","doi-asserted-by":"crossref","first-page":"6053","DOI":"10.1007\/s40314-018-0679-2","volume":"37","author":"K Parand","year":"2018","unstructured":"Parand K, Bahramnezhad A, Farahani H (2018) A numerical method based on rational Gegenbauer functions for solving boundary layer flow of a Powell\u2013Eyring non-Newtonian fluid. Comput Appl Math 37:6053\u20136075","journal-title":"Comput Appl Math"},{"key":"727_CR44","first-page":"340","volume":"67","author":"AH Bhrawy","year":"2015","unstructured":"Bhrawy AH, Zaky MA, Baleanu D (2015) New numerical approximations for space- time fractional Burgers\u2019 equations via a Legendre spectral-collocation method. Rom Rep Phys 67:340\u2013349","journal-title":"Rom Rep Phys"},{"key":"727_CR45","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/s11075-012-9598-2","volume":"62","author":"C Allouch","year":"2013","unstructured":"Allouch C, Sablonniere P, Sbibih D (2013) A collocation method for the numerical solution of a two dimensional integral equation using a quadratic spline quasi-interpolant. Numer Algorithms 62:445\u2013468","journal-title":"Numer Algorithms"},{"issue":"4","key":"727_CR46","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1007\/s40324-016-0103-z","volume":"74","author":"K Parand","year":"2017","unstructured":"Parand K, Mazaheri P, Delkhosh M, Ghaderi A (2017) New numerical solutions for solving Kidder equation by using the rational Jacobi functions. SeMA J 74(4):569\u2013583","journal-title":"SeMA J"},{"issue":"1","key":"727_CR47","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1140\/epjp\/i2018-11859-5","volume":"133","author":"K Parand","year":"2018","unstructured":"Parand K, Latifi S, Delkhosh M, Moayeri MM (2018) Generalized Lagrangian Jacobi Gauss collocation method for solving unsteady isothermal gas through a micro-nano porous medium. Eur Phys J Plus 133(1):28","journal-title":"Eur Phys J Plus"},{"key":"727_CR48","first-page":"15","volume":"1","author":"A Borhanifar","year":"2014","unstructured":"Borhanifar A, Sadri K (2014) Numerical solution for systems of two dimensional integral equations by using Jacobi operational collocation method. Sohag J Math 1:15\u201326","journal-title":"Sohag J Math"},{"key":"727_CR49","volume-title":"Numerical analysis","author":"RL Burden","year":"2001","unstructured":"Burden RL, Faires JD (2001) Numerical analysis. Youngstown State University, Youngstown"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-019-00727-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00366-019-00727-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-019-00727-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,16]],"date-time":"2024-07-16T15:41:42Z","timestamp":1721144502000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00366-019-00727-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,3]]},"references-count":49,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,4]]}},"alternative-id":["727"],"URL":"https:\/\/doi.org\/10.1007\/s00366-019-00727-y","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,4,3]]},"assertion":[{"value":"26 October 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 February 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 April 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}