LEADER 01146cam0 2200301 450 001 E600200057763 005 20160421150715.0 100 $a20091215d1991 |||||ita|0103 ba 101 $aita 102 $aIT 200 1 $aEstate tragica e grave$f[Franco Casavola] 210 $aRoma$cEdizioni Studiuim$d[1991?] 215 $ap. 470-476$d23 cm 300 $a(mm) 300 $aEstr. da.: Studium, n. 4 (1991) 300 $aAltro esempl. in: Fondo Casavola Opusc. 51/b 700 1$aCasavola$b, Francesco Paolo$3A600200040546$4070$0189715 801 0$aIT$bUNISOB$c20160421$gRICA 850 $aUNISOB 852 $aUNISOB$jFondo|Casavola|Opusc$m145286 852 $aUNISOB$jFondo|Casavola|Opusc$m145298 912 $aE600200057763 940 $aM 102 Monografia moderna SBN 941 $aM 957 $aFondo|Casavola|Opusc$b000051$gSi$d145286$hCasavola$rdono$1menle$2UNISOB$3UNISOB$420091215102355.0$520160421150632.0$6petrellap 957 $aFondo|Casavola|Opusc$b000051$i-b$gSI$d145298$hCasavola$rDono$1petrellap$2UNISOB$3UNISOB$420160421150636.0$520160421150715.0$6petrellap 996 $aEstate tragica e grave$91707426 997 $aUNISOB LEADER 04721 am 22007453u 450 001 9910160767603321 005 20230125193845.0 010 $a3-319-32726-7 024 7 $a10.1007/978-3-319-32726-6 035 $a(CKB)3710000000734708 035 $a(DE-He213)978-3-319-32726-6 035 $a(MiAaPQ)EBC5579071 035 $a(Au-PeEL)EBL5579071 035 $a(OCoLC)952470674 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/31761 035 $a(PPN)194380866 035 $a(EXLCZ)993710000000734708 100 $a20160615d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aScaling of Differential Equations$b[electronic resource] /$fby Hans Petter Langtangen, Geir K. Pedersen 205 $a1st ed. 2016. 210 $aCham$cSpringer Nature$d2016 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XIII, 138 p. 22 illus.) 225 1 $aSimula SpringerBriefs on Computing,$x2512-1677 ;$v2 311 $a3-319-32725-9 327 $aPreface -- 1 Dimensions and Units -- 2 Ordinary Differential Equations Models -- 3 Basic Partial Differential Equations Models -- Advanced Partial Differential Equations Models -- References -- Index. 330 $aThe book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and example-driven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically. This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations. 410 0$aSimula SpringerBriefs on Computing,$x2512-1677 ;$v2 606 $aDifferential equations 606 $aPartial differential equations 606 $aMathematical models 606 $aComputer mathematics 606 $aComputer simulation 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aMathematical Modeling and Industrial Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M14068 606 $aComputational Science and Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/M14026 606 $aSimulation and Modeling$3https://scigraph.springernature.com/ontologies/product-market-codes/I19000 610 $aDifferential equations 610 $aSimulation and modeling 615 0$aDifferential equations. 615 0$aPartial differential equations. 615 0$aMathematical models. 615 0$aComputer mathematics. 615 0$aComputer simulation. 615 14$aOrdinary Differential Equations. 615 24$aPartial Differential Equations. 615 24$aMathematical Modeling and Industrial Mathematics. 615 24$aComputational Science and Engineering. 615 24$aSimulation and Modeling. 676 $a515.352 700 $aLangtangen$b Hans Petter$4aut$4http://id.loc.gov/vocabulary/relators/aut$022965 702 $aPedersen$b Geir K$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910160767603321 996 $aScaling of Differential Equations$92234765 997 $aUNINA