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Question: area under pdsolve diagram

Question: area under pdsolve diagram

mehdi jafari 749 Maple
integration area pdsolve
June 19 2017
0

i want to know the area under a diagram plotted by pdsolve, how can i do that? for example in below , what is the area under p1 diagram?


 

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restart:k:=5;

5

 (1)
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EQ:=diff(u(x,t),t)=k*diff(u(x,t),x$2);

diff(u(x, t), t) = 5*(diff(diff(u(x, t), x), x))

 (2)
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ibc:=u(0,t)=0,u(1,t)=0, u(x,0) = x;

u(0, t) = 0, u(1, t) = 0, u(x, 0) = x

 (3)
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sol:=pdsolve({EQ},{ibc},numeric);

_m2021168030176

 (4)
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p1:=sol:-plot(u,x=0.5,t=0...10,style = line,color = "Blue",legend = "heat Plot",axes=boxed);

 
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M:=op(1,op(1,p1));

M := Array(1..201, 1..2, {(1, 1) = .0, (1, 2) = .5, (2, 1) = 0.5e-1, (2, 2) = .2702110502740721, (3, 1) = .1, (3, 2) = -0.176887059080428e-1, (4, 1) = .15, (4, 2) = -0.6515347962762406e-2, (5, 1) = .2, (5, 2) = 0.74109221595503715e-2, (6, 1) = .25, (6, 2) = -0.6178984348254404e-2, (7, 1) = .3, (7, 2) = 0.49645329554988925e-2, (8, 1) = .35, (8, 2) = -0.3948699801548904e-2, (9, 1) = .4, (9, 2) = 0.31161325326115076e-2, (10, 1) = .45, (10, 2) = -0.24369292293079273e-2, (11, 1) = .5, (11, 2) = 0.18845070914387395e-2, (12, 1) = .55, (12, 2) = -0.14366378752131666e-2, (13, 1) = .6, (13, 2) = 0.10748767238662861e-2, (14, 1) = .65, (14, 2) = -0.7839388660633711e-3, (15, 1) = .7, (15, 2) = 0.5511660027174686e-3, (16, 1) = .75, (16, 2) = -0.3660810752890637e-3, (17, 1) = .8, (17, 2) = 0.22001797006812284e-3, (18, 1) = .85, (18, 2) = -0.10581369353881973e-3, (19, 1) = .9, (19, 2) = 0.1755251750102873e-4, (20, 1) = .95, (20, 2) = 0.4964665498398858e-4, (21, 1) = 1.0, (21, 2) = -0.9980698165105276e-4, (22, 1) = 1.05, (22, 2) = 0.1362404856962589e-3, (23, 1) = 1.1, (23, 2) = -0.16167000912668705e-3, (24, 1) = 1.15, (24, 2) = 0.17833050358069153e-3, (25, 1) = 1.2, (25, 2) = -0.18805314257842951e-3, (26, 1) = 1.25, (26, 2) = 0.19233515285281392e-3, (27, 1) = 1.3, (27, 2) = -0.19239777469550633e-3, (28, 1) = 1.35, (28, 2) = 0.18923435555607597e-3, (29, 1) = 1.4, (29, 2) = -0.18365024366673088e-3, (30, 1) = 1.45, (30, 2) = 0.17629586775928352e-3, (31, 1) = 1.5, (31, 2) = -0.16769415545232156e-3, (32, 1) = 1.55, (32, 2) = 0.15826324867687376e-3, (33, 1) = 1.6, (33, 2) = -0.1483353129733858e-3, (34, 1) = 1.65, (34, 2) = 0.1381721031382132e-3, (35, 1) = 1.7, (35, 2) = -0.12797783595325005e-3, (36, 1) = 1.75, (36, 2) = 0.11790982779578369e-3, (37, 1) = 1.8, (37, 2) = -0.10808727763435372e-3, (38, 1) = 1.85, (38, 2) = 0.9859851163881829e-4, (39, 1) = 1.9, (39, 2) = -0.8950695218043435e-4, (40, 1) = 1.95, (40, 2) = 0.8085602954949057e-4, (41, 1) = 2.0, (41, 2) = -0.7267321775920382e-4, (42, 1) = 2.05, (42, 2) = 0.6497334507523223e-4, (43, 1) = 2.1, (43, 2) = -0.5776130436199765e-4, (44, 1) = 2.15, (44, 2) = 0.5103426709812118e-4, (45, 1) = 2.2, (45, 2) = -0.4478348725852213e-4, (46, 1) = 2.25, (46, 2) = 0.3899576658643508e-4, (47, 1) = 2.3, (47, 2) = -0.336546405833609e-4, (48, 1) = 2.35, (48, 2) = 0.28741334410836633e-4, (49, 1) = 2.4, (49, 2) = -0.2423552947809686e-4, (50, 1) = 2.45, (50, 2) = 0.20115974495047912e-4, (51, 1) = 2.5, (51, 2) = -0.16360968960468515e-4, (52, 1) = 2.55, (52, 2) = 0.12948742231058999e-4, (53, 1) = 2.6, (53, 2) = -0.985774731176686e-5, (54, 1) = 2.65, (54, 2) = 0.706688518346671e-5, (55, 1) = 2.7, (55, 2) = -0.4555672725651303e-5, (56, 1) = 2.75, (56, 2) = 0.23043650036730538e-5, (57, 1) = 2.8, (57, 2) = -0.29404079279315267e-6, (58, 1) = 2.85, (58, 2) = -0.14933413612624144e-5, (59, 1) = 2.9, (59, 2) = 0.30749105483557417e-5, (60, 1) = 2.95, (60, 2) = -0.4466869448461453e-5, (61, 1) = 3.0, (61, 2) = 0.5684494809229467e-5, (62, 1) = 3.05, (62, 2) = -0.67421491593684444e-5, (63, 1) = 3.1, (63, 2) = 0.765330108066053e-5, (64, 1) = 3.15, (64, 2) = -0.8430551865031369e-5, (65, 1) = 3.2, (65, 2) = 0.9085666798487518e-5, (66, 1) = 3.25, (66, 2) = -0.9629609655930039e-5, (67, 1) = 3.3, (67, 2) = 0.10072579272402201e-4, (68, 1) = 3.35, (68, 2) = -0.1042404728762369e-4, (69, 1) = 3.4, (69, 2) = 0.1069279635035891e-4, (70, 1) = 3.45, (70, 2) = -0.10886958224421352e-4, (71, 1) = 3.5, (71, 2) = 0.11014051364892259e-4, (72, 1) = 3.55, (72, 2) = -0.11081017636391213e-4, (73, 1) = 3.6, (73, 2) = 0.11094257929051255e-4, (74, 1) = 3.65, (74, 2) = -0.11059666495657345e-4, (75, 1) = 3.7, (75, 2) = 0.109826638880031e-4, (76, 1) = 3.75, (76, 2) = -0.10868228414258878e-4, (77, 1) = 3.8, (77, 2) = 0.10720926073958364e-4, (78, 1) = 3.85, (78, 2) = -0.1054493895470911e-4, (79, 1) = 3.9, (79, 2) = 0.1034409209623252e-4, (80, 1) = 3.95, (80, 2) = -0.10121878843963985e-4, (81, 1) = 4.0, (81, 2) = 0.9881484727059153e-5, (82, 1) = 4.05, (82, 2) = -0.9625809905064345e-5, (83, 1) = 4.1, (83, 2) = 0.9357490234275213e-5, (84, 1) = 4.15, (84, 2) = -0.9078917009490728e-5, (85, 1) = 4.2, (85, 2) = 0.87922554398473e-5, (86, 1) = 4.25, (86, 2) = -0.8499461919063325e-5, (87, 1) = 4.3, (87, 2) = 0.8202300151001906e-5, (88, 1) = 4.35, (88, 2) = -0.7902356191213331e-5, (89, 1) = 4.4, (89, 2) = 0.7601052464222056e-5, (90, 1) = 4.45, (90, 2) = -0.72996608149495766e-5, (91, 1) = 4.5, (91, 2) = 0.699931465092186e-5, (92, 1) = 4.55, (92, 2) = -0.6701020229904285e-5, (93, 1) = 4.6, (93, 2) = 0.6405667145430395e-5, (94, 1) = 4.65, (94, 2) = -0.6114038060383664e-5, (95, 1) = 4.7, (95, 2) = 0.5826817736440689e-5, (96, 1) = 4.75, (96, 2) = -0.5544601404792595e-5, (97, 1) = 4.8, (97, 2) = 0.52679025211894145e-5, (98, 1) = 4.85, (98, 2) = -0.4997159946020307e-5, (99, 1) = 4.9, (99, 2) = 0.47327445878452e-5, (100, 1) = 4.95, (100, 2) = -0.4474965546586055e-5, (101, 1) = 5.0, (101, 2) = 0.4224075790442743e-5, (102, 1) = 5.05, (102, 2) = -0.3980277398539528e-5, (103, 1) = 5.1, (103, 2) = 0.3743726399348483e-5, (104, 1) = 5.15, (104, 2) = -0.35145372330544755e-5, (105, 1) = 5.2, (105, 2) = 0.3292786864253045e-5, (106, 1) = 5.25, (106, 2) = -0.3078518569671755e-5, (107, 1) = 5.3, (107, 2) = 0.28717454240173786e-5, (108, 1) = 5.35, (108, 2) = -0.2672453505531053e-5, (109, 1) = 5.4, (109, 2) = 0.2480604841418905e-5, (110, 1) = 5.45, (110, 2) = -0.22961401119743008e-5, (111, 1) = 5.5, (111, 2) = 0.21189811309571416e-5, (112, 1) = 5.55, (112, 2) = -0.19490331186010634e-5, (113, 1) = 5.6, (113, 2) = 0.17861867825155937e-5, (114, 1) = 5.65, (114, 2) = -0.16303202207033257e-5, (115, 1) = 5.7, (115, 2) = 0.14813006599365237e-5, (116, 1) = 5.75, (116, 2) = -0.13389860418240196e-5, (117, 1) = 5.8, (117, 2) = 0.12032264680435905e-5, (118, 1) = 5.85, (118, 2) = -0.10738655154134225e-5, (119, 1) = 5.9, (119, 2) = 0.9507414307327055e-6, (120, 1) = 5.95, (120, 2) = -0.8336882146176523e-6, (121, 1) = 6.0, (121, 2) = 0.7225366029120385e-6, (122, 1) = 6.05, (122, 2) = -0.6171149536407717e-6, (123, 1) = 6.1, (123, 2) = 0.5172500469062582e-6, (124, 1) = 6.15, (124, 2) = -0.422767804599377e-6, (125, 1) = 6.2, (125, 2) = 0.3334939363034557e-6, (126, 1) = 6.25, (126, 2) = -0.24925451730719557e-6, (127, 1) = 6.3, (127, 2) = 0.1698765042164462e-6, (128, 1) = 6.35, (128, 2) = -0.9518819325289293e-7, (129, 1) = 6.4, (129, 2) = 0.25019625957658297e-7, (130, 1) = 6.45, (130, 2) = 0.4079705332935711e-7, (131, 1) = 6.5, (131, 2) = -0.10242728416703212e-6, (132, 1) = 6.55, (132, 2) = 0.16003381713738053e-6, (133, 1) = 6.6, (133, 2) = -0.21377647792892648e-6, (134, 1) = 6.65, (134, 2) = 0.2638119651684455e-6, (135, 1) = 6.7, (135, 2) = -0.31029367903289395e-6, (136, 1) = 6.75, (136, 2) = 0.3533715778983202e-6, (137, 1) = 6.8, (137, 2) = -0.3931920604894687e-6, (138, 1) = 6.85, (138, 2) = 0.4298978711906126e-6, (139, 1) = 6.9, (139, 2) = -0.4636280263535863e-6, (140, 1) = 6.95, (140, 2) = 0.494517759612214e-6, (141, 1) = 7.0, (141, 2) = -0.5226984843620009e-6, (142, 1) = 7.05, (142, 2) = 0.5482977717131691e-6, (143, 1) = 7.1, (143, 2) = -0.5714393423533197e-6, (144, 1) = 7.15, (144, 2) = 0.5922430708876365e-6, (145, 1) = 7.2, (145, 2) = -0.610825001331253e-6, (146, 1) = 7.25, (146, 2) = 0.6272973725430698e-6, (147, 1) = 7.3, (147, 2) = -0.641768652482882e-6, (148, 1) = 7.35, (148, 2) = 0.6543435802710991e-6, (149, 1) = 7.4, (149, 2) = -0.6651232151103739e-6, (150, 1) = 7.45, (150, 2) = 0.6742049912106031e-6, (151, 1) = 7.5, (151, 2) = -0.6816827779311618e-6, (152, 1) = 7.55, (152, 2) = 0.6876469444194619e-6, (153, 1) = 7.6, (153, 2) = -0.6921844280904861e-6, (154, 1) = 7.65, (154, 2) = 0.6953788063481056e-6, (155, 1) = 7.7, (155, 2) = -0.6973103710014924e-6, (156, 1) = 7.75, (156, 2) = 0.6980562048815929e-6, (157, 1) = 7.8, (157, 2) = -0.6976902602061175e-6, (158, 1) = 7.85, (158, 2) = 0.6962834382846133e-6, (159, 1) = 7.9, (159, 2) = -0.6939036701932665e-6, (160, 1) = 7.95, (160, 2) = 0.690615998086224e-6, (161, 1) = 8.0, (161, 2) = -0.6864826568410622e-6, (162, 1) = 8.05, (162, 2) = 0.6815631557688252e-6, (163, 1) = 8.1, (163, 2) = -0.6759143601450263e-6, (164, 1) = 8.15, (164, 2) = 0.669590572344911e-6, (165, 1) = 8.2, (165, 2) = -0.6626436123890619e-6, (166, 1) = 8.25, (166, 2) = 0.6551228977290213e-6, (167, 1) = 8.3, (167, 2) = -0.647075522119317e-6, (168, 1) = 8.35, (168, 2) = 0.6385463334437125e-6, (169, 1) = 8.4, (169, 2) = -0.629578010378859e-6, (170, 1) = 8.45, (170, 2) = 0.6202111377936157e-6, (171, 1) = 8.5, (171, 2) = -0.6104842807971703e-6, (172, 1) = 8.55, (172, 2) = 0.6004340573606388e-6, (173, 1) = 8.6, (173, 2) = -0.5900952094508935e-6, (174, 1) = 8.65, (174, 2) = 0.5795006726227363e-6, (175, 1) = 8.7, (175, 2) = -0.5686816440282655e-6, (176, 1) = 8.75, (176, 2) = 0.5576676488088356e-6, (177, 1) = 8.8, (177, 2) = -0.5464866048451384e-6, (178, 1) = 8.85, (178, 2) = 0.5351648858455677e-6, (179, 1) = 8.9, (179, 2) = -0.5237273827621483e-6, (180, 1) = 8.95, (180, 2) = 0.5121975635274654e-6, (181, 1) = 9.0, (181, 2) = -0.5005975311119593e-6, (182, 1) = 9.05, (182, 2) = 0.488948079906314e-6, (183, 1) = 9.1, (183, 2) = -0.4772687504359755e-6, (184, 1) = 9.15, (184, 2) = 0.46557788242095225e-6, (185, 1) = 9.2, (185, 2) = -0.45389266619653036e-6, (186, 1) = 9.25, (186, 2) = 0.4422291925122823e-6, (187, 1) = 9.3, (187, 2) = -0.43060250073186364e-6, (188, 1) = 9.35, (188, 2) = 0.4190266254556287e-6, (189, 1) = 9.4, (189, 2) = -0.4075146415927183e-6, (190, 1) = 9.45, (190, 2) = 0.39607870790862633e-6, (191, 1) = 9.5, (191, 2) = -0.38473010907775763e-6, (192, 1) = 9.55, (192, 2) = 0.37347929627010353e-6, (193, 1) = 9.6, (193, 2) = -0.362335926303425e-6, (194, 1) = 9.65, (194, 2) = 0.35130889939221703e-6, (195, 1) = 9.7, (195, 2) = -0.34040639552618525e-6, (196, 1) = 9.75, (196, 2) = 0.3296359095107469e-6, (197, 1) = 9.8, (197, 2) = -0.3190042847032402e-6, (198, 1) = 9.85, (198, 2) = 0.30851774547799635e-6, (199, 1) = 9.9, (199, 2) = -0.29818192845446557e-6, (200, 1) = 9.95, (200, 2) = 0.2880019125209349e-6, (201, 1) = 10.0, (201, 2) = -0.2779822476886622e-6}, datatype = float[8], order = C_order)

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