1060:
894:
834:
959:
986:
708:
449:
192:
323:
1002:
364:
1222:
1163:
254:
701:
156:
575:
229:
839:
250:
202:
318:
237:
212:
1095:
694:
629:
354:
793:
753:
729:
272:
182:
369:
913:
733:
197:
187:
1244:
644:
495:
285:
207:
919:
767:
or
Dirichlet boundary condition is defined by weighted-integral form of a differential equation. The dependent unknown
330:
245:
535:
1153:
1141:
403:
506:
1133:
649:
484:
1158:
1137:
1123:
for viscous fluids states that at a solid boundary, the fluid will have zero velocity relative to the boundary.
500:
408:
799:
562:
760:
580:
570:
518:
359:
1210:
1087:
1067:
393:
639:
624:
513:
456:
438:
277:
33:
525:
461:
434:
737:
557:
542:
443:
307:
146:
113:
104:
964:
552:
547:
430:
744:. In the sciences and engineering, a Dirichlet boundary condition may also be referred to as a
1218:
1120:
1091:
741:
664:
609:
388:
123:
1183:
Cheng, A.; Cheng, D. T. (2005). "Heritage and early history of the boundary element method".
740:
of the domain are fixed. The question of finding solutions to such equations is known as the
17:
1192:
989:
674:
659:
614:
530:
57:
669:
1213:(2009). "Second order differential equations in one dimension: Finite element models".
1116:
1109:
634:
619:
425:
413:
132:
1196:
1238:
1102:
654:
604:
490:
118:
62:
1082:
For example, the following would be considered
Dirichlet boundary conditions:
679:
420:
141:
84:
74:
95:
90:
79:
836:
the
Dirichlet boundary conditions on the interval take the form
1098:), where one end of a beam is held at a fixed position in space.
1055:{\displaystyle y(x)=f(x)\quad \forall x\in \partial \Omega ,}
1132:
Many other boundary conditions are possible, including the
736:, such that the values that the solution takes along the
27:
Type of constraint on solutions to differential equations
1112:, where a node of a circuit is held at a fixed voltage.
1005:
967:
922:
842:
802:
1140:. The latter is a combination of the Dirichlet and
1217:(3rd ed.). Boston: McGraw-Hill. p. 110.
1054:
980:
953:
888:
828:
1105:, where a surface is held at a fixed temperature.
771:appearing in the boundary expression is termed a
992:, the Dirichlet boundary conditions on a domain
889:{\displaystyle y(a)=\alpha ,\quad y(b)=\beta ,}
702:
8:
1215:An Introduction to the Finite Element Method
1185:Engineering Analysis with Boundary Elements
769:u in the same form as the weight function w
709:
695:
175:
50:
29:
1004:
972:
966:
927:
921:
841:
801:
775:, and its specification constitutes the
1175:
590:
341:
263:
221:
164:
131:
103:
53:
39:
32:
1164:Boundary conditions in fluid dynamics
7:
750:boundary condition of the first type
157:List of named differential equations
230:Dependent and independent variables
1046:
1043:
1034:
969:
924:
779:or Dirichlet boundary condition.
25:
1197:10.1016/j.enganabound.2004.12.001
954:{\displaystyle \nabla ^{2}y+y=0,}
365:Carathéodory's existence theorem
1033:
864:
1030:
1024:
1015:
1009:
874:
868:
852:
846:
794:ordinary differential equation
754:Peter Gustav Lejeune Dirichlet
452: / Integral solutions
1:
914:partial differential equation
734:partial differential equation
18:Dirichlet boundary conditions
496:Exponential response formula
242:Coupled / Decoupled
981:{\displaystyle \nabla ^{2}}
1261:
1154:Neumann boundary condition
1134:Cauchy boundary condition
1128:Other boundary conditions
630:JĂłzef Maria Hoene-WroĆski
576:Undetermined coefficients
485:Method of characteristics
370:CauchyâKowalevski theorem
1159:Robin boundary condition
1138:mixed boundary condition
1070:defined on the boundary
829:{\displaystyle y''+y=0,}
746:fixed boundary condition
355:PicardâLindelöf theorem
349:Existence and uniqueness
761:finite-element analysis
581:Variation of parameters
571:Separation of variables
360:Peano existence theorem
1088:mechanical engineering
1056:
982:
955:
890:
830:
650:Carl David Tolmé Runge
193:Differential-algebraic
34:Differential equations
1057:
983:
956:
891:
831:
640:Augustin-Louis Cauchy
625:Joseph-Louis Lagrange
457:Numerical integration
439:Exponential stability
302:Relation to processes
1003:
965:
920:
840:
800:
752:. It is named after
721:In mathematics, the
462:Dirac delta function
198:Integro-differential
1245:Boundary conditions
904:are given numbers.
558:Perturbation theory
553:Integral transforms
444:Rate of convergence
310:(discrete analogue)
147:Population dynamics
114:Continuum mechanics
105:Applied mathematics
1052:
978:
951:
886:
826:
726:boundary condition
548:Integrating factor
389:Initial conditions
324:Stochastic partial
1224:978-0-07-126761-8
1121:no-slip condition
1092:civil engineering
742:Dirichlet problem
728:is imposed on an
719:
718:
610:Gottfried Leibniz
501:Finite difference
293:
292:
154:
153:
124:Dynamical systems
16:(Redirected from
1252:
1229:
1228:
1207:
1201:
1200:
1180:
1073:
1065:
1061:
1059:
1058:
1053:
998:
990:Laplace operator
987:
985:
984:
979:
977:
976:
960:
958:
957:
952:
932:
931:
903:
899:
895:
893:
892:
887:
835:
833:
832:
827:
810:
796:, for instance,
773:primary variable
711:
704:
697:
675:Phyllis Nicolson
660:Rudolf Lipschitz
543:Green's function
519:Infinite element
510:
475:Solution methods
453:
311:
222:By variable type
176:
58:Natural sciences
51:
30:
21:
1260:
1259:
1255:
1254:
1253:
1251:
1250:
1249:
1235:
1234:
1233:
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1225:
1209:
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1177:
1172:
1150:
1130:
1080:
1071:
1063:
1001:
1000:
993:
968:
963:
962:
923:
918:
917:
916:, for example,
910:
901:
897:
838:
837:
803:
798:
797:
790:
785:
715:
686:
685:
684:
615:Jacob Bernoulli
599:
586:
585:
567:
536:PetrovâGalerkin
504:
489:
476:
468:
467:
466:
448:
394:Boundary values
383:
375:
374:
350:
337:
336:
335:
309:
303:
295:
294:
282:
259:
217:
173:
160:
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133:Social sciences
89:
67:
48:
28:
23:
22:
15:
12:
11:
5:
1258:
1256:
1248:
1247:
1237:
1236:
1231:
1230:
1223:
1202:
1191:(3): 268â302.
1174:
1173:
1171:
1168:
1167:
1166:
1161:
1156:
1149:
1146:
1129:
1126:
1125:
1124:
1117:fluid dynamics
1113:
1110:electrostatics
1106:
1099:
1079:
1076:
1051:
1048:
1045:
1042:
1039:
1036:
1032:
1029:
1026:
1023:
1020:
1017:
1014:
1011:
1008:
999:take the form
975:
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950:
947:
944:
941:
938:
935:
930:
926:
909:
906:
885:
882:
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867:
863:
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851:
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789:
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717:
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683:
682:
677:
672:
667:
665:Ernst Lindelöf
662:
657:
652:
647:
642:
637:
635:Joseph Fourier
632:
627:
622:
620:Leonhard Euler
617:
612:
607:
601:
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597:
596:
593:
592:
588:
587:
584:
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578:
573:
566:
565:
560:
555:
550:
545:
540:
539:
538:
528:
523:
522:
521:
514:Finite element
511:
507:CrankâNicolson
498:
493:
487:
482:
478:
477:
474:
473:
470:
469:
465:
464:
459:
454:
446:
441:
428:
426:Phase portrait
423:
418:
417:
416:
414:Cauchy problem
411:
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391:
385:
384:
382:General topics
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291:
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257:
255:Nonhomogeneous
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165:Classification
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54:
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26:
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14:
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10:
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3:
2:
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1190:
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1179:
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1169:
1165:
1162:
1160:
1157:
1155:
1152:
1151:
1147:
1145:
1143:
1139:
1135:
1127:
1122:
1118:
1114:
1111:
1107:
1104:
1103:heat transfer
1100:
1097:
1093:
1089:
1085:
1084:
1083:
1077:
1075:
1069:
1049:
1040:
1037:
1027:
1021:
1018:
1012:
1006:
997:
991:
973:
948:
945:
942:
939:
936:
933:
928:
915:
907:
905:
883:
880:
877:
871:
865:
861:
858:
855:
849:
843:
823:
820:
817:
814:
811:
807:
804:
795:
787:
782:
780:
778:
774:
770:
766:
762:
757:
756:(1805â1859).
755:
751:
747:
743:
739:
735:
731:
727:
724:
712:
707:
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690:
689:
681:
678:
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633:
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626:
623:
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618:
616:
613:
611:
608:
606:
603:
602:
595:
594:
589:
582:
579:
577:
574:
572:
569:
568:
564:
561:
559:
556:
554:
551:
549:
546:
544:
541:
537:
534:
533:
532:
529:
527:
526:Finite volume
524:
520:
517:
516:
515:
512:
508:
502:
499:
497:
494:
492:
488:
486:
483:
480:
479:
472:
471:
463:
460:
458:
455:
451:
447:
445:
442:
440:
436:
432:
429:
427:
424:
422:
419:
415:
412:
410:
407:
405:
402:
400:
397:
396:
395:
392:
390:
387:
386:
379:
378:
371:
368:
366:
363:
361:
358:
356:
353:
352:
346:
345:
340:
332:
329:
325:
322:
321:
320:
317:
316:
312:
306:
305:
299:
298:
287:
284:
283:
279:
276:
274:
271:
270:
268:
267:
262:
256:
252:
249:
247:
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231:
228:
227:
226:
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196:
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186:
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181:
180:
178:
177:
169:
168:
163:
158:
148:
145:
143:
140:
139:
138:
137:
134:
130:
125:
122:
120:
117:
115:
112:
111:
110:
109:
106:
102:
97:
94:
92:
88:
86:
83:
81:
78:
76:
73:
72:
71:
70:
64:
61:
59:
56:
55:
52:
44:
43:
38:
35:
31:
19:
1214:
1211:Reddy, J. N.
1205:
1188:
1184:
1178:
1144:conditions.
1131:
1081:
1078:Applications
995:
988:denotes the
911:
791:
776:
772:
768:
764:
758:
749:
745:
725:
722:
720:
670:Ămile Picard
655:Martin Kutta
645:George Green
605:Isaac Newton
437: /
433: /
398:
253: /
119:Chaos theory
1096:beam theory
1066:is a known
563:RungeâKutta
308:Difference
251:Homogeneous
63:Engineering
1170:References
680:John Crank
481:Inspection
435:Asymptotic
319:Stochastic
238:Autonomous
213:Non-linear
203:Fractional
1047:Ω
1044:∂
1041:∈
1035:∀
970:∇
925:∇
881:β
859:α
777:essential
765:essential
723:Dirichlet
421:Wronskian
399:Dirichlet
142:Economics
85:Chemistry
75:Astronomy
1239:Category
1148:See also
1136:and the
1068:function
808:″
783:Examples
738:boundary
730:ordinary
531:Galerkin
431:Lyapunov
342:Solution
286:Notation
278:Operator
264:Features
183:Ordinary
1142:Neumann
792:For an
404:Neumann
188:Partial
96:Geology
91:Biology
80:Physics
1221:
1119:, the
1062:where
961:where
912:For a
896:where
763:, the
591:People
503:
450:Series
208:Linear
47:Fields
491:Euler
409:Robin
331:Delay
273:Order
246:Exact
172:Types
40:Scope
1219:ISBN
1090:and
994:Ω â
900:and
598:List
1193:doi
1115:In
1108:In
1101:In
1086:In
908:PDE
788:ODE
759:In
748:or
732:or
1241::
1189:29
1187:.
1074:.
1072:âΩ
1227:.
1199:.
1195::
1094:(
1064:f
1050:,
1038:x
1031:)
1028:x
1025:(
1022:f
1019:=
1016:)
1013:x
1010:(
1007:y
996:R
974:2
949:,
946:0
943:=
940:y
937:+
934:y
929:2
902:ÎČ
898:α
884:,
878:=
875:)
872:b
869:(
866:y
862:,
856:=
853:)
850:a
847:(
844:y
824:,
821:0
818:=
815:y
812:+
805:y
710:e
703:t
696:v
509:)
505:(
20:)
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