LEADER 03452nam 22005895 450 001 9910992785103321 005 20250329192713.0 010 $a9783031850561 010 $a3031850564 024 7 $a10.1007/978-3-031-85056-1 035 $a(CKB)38166497700041 035 $a(DE-He213)978-3-031-85056-1 035 $a(MiAaPQ)EBC31979962 035 $a(Au-PeEL)EBL31979962 035 $a(EXLCZ)9938166497700041 100 $a20250329d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNeural Network Methods for Dynamic Equations on Time Scales /$fby Svetlin Georgiev 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (VIII, 112 p. 38 illus., 34 illus. in color.) 225 1 $aSpringerBriefs in Computational Intelligence,$x2625-3712 311 08$a9783031850554 311 08$a3031850556 327 $aIntroduction -- Multilayer Artificial Neural Networks -- Regression Based Artificial Neural Networks -- Chebyshev Neural Networks -- Legendre Neural Networks -- Index. 330 $aThis book aims to handle dynamic equations on time scales using artificial neural network (ANN). Basic facts and methods for ANN modeling are considered. The multilayer artificial neural network (ANN) model is introduced for solving of dynamic equations on arbitrary time scales. A multilayer ANN model with one input layer containing a single node, a hidden layer with m nodes, and one output node are investigated. The feed-forward neural network model and unsupervised error back-propagation algorithm are developed. Modification of network parameters is done without the use of any optimization technique. The regression-based neural network (RBNN) model is introduced for solving dynamic equations on arbitrary time scales. The RBNN trial solution of dynamic equations is obtained by using the RBNN model for single input and single output system. A variety of initial and boundary value problems are solved. The Chebyshev neural network (ChNN) model and Levendre neural network model are developed. The ChNN trial solution of dynamic equations is obtained by using the ChNN model for single input and single output system. This book is addressed to a wide audience of specialists such as mathematicians, physicists, engineers, and biologists. It can be used as a textbook at the graduate level and as a reference book for several disciplines. 410 0$aSpringerBriefs in Computational Intelligence,$x2625-3712 606 $aComputational intelligence 606 $aEngineering mathematics 606 $aArtificial intelligence 606 $aComputational Intelligence 606 $aEngineering Mathematics 606 $aArtificial Intelligence 615 0$aComputational intelligence. 615 0$aEngineering mathematics. 615 0$aArtificial intelligence. 615 14$aComputational Intelligence. 615 24$aEngineering Mathematics. 615 24$aArtificial Intelligence. 676 $a006.3 700 $aGeorgiev$b Svetlin$4aut$4http://id.loc.gov/vocabulary/relators/aut$01218802 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910992785103321 996 $aNeural Network Methods for Dynamic Equations on Time Scales$94349050 997 $aUNINA