Solving differential equations using Euler's method in Org tables

euler_method.org

$$w’ = (3-w)(w+1)$$

t	w	m	1
0	4	-5
1	-1	0
2	-1	0
3	-1	0

$$y’ = e^2/y$$

t	y	m	0.5
0	2	2.7182818
0.5	3.3591409	1.8137388
1.	4.2660103	1.5981107
1.5	5.0650657	1.4841788
2.	5.8071551	1.4111468
2.5	6.5127285	1.3594646
3.	7.1924608	1.3205772

$$ y’ = y^2 - y^3 $$

t	y	m	0.1
0	0.2	0.032
0.1	0.2032	0.032900063
0.2	0.20649001	0.033833778
0.3	0.20987339	0.034802580
0.4	0.21335365	0.035807969
0.5	0.21693445	0.036851500
0.6	0.2206196	0.037934788
0.7	0.22441308	0.039059512
0.8	0.22831903	0.040227404
0.9	0.23234177	0.041440262
1.	0.23648580	0.042699939
1.1	0.24075579	0.044008338
1.2	0.24515662	0.045367422
1.3	0.24969336	0.046779199
1.4	0.25437128	0.048245718
1.5	0.25919585	0.049769066
1.6	0.26417276	0.051351357
1.7	0.26930790	0.052994720
1.8	0.27460737	0.054701283
1.9	0.28007750	0.056473173
2.	0.28572482	0.058312478
2.1	0.29155607	0.060221235
2.2	0.29757819	0.062201403
2.3	0.30379833	0.064254837
2.4	0.31022381	0.066383241
2.5	0.31686213	0.068588142
2.6	0.32372094	0.070870831
2.7	0.33080802	0.073232319
2.8	0.33813125	0.075673269
2.9	0.34569858	0.078193932
3.	0.35351797	0.080794063
3.1	0.36159738	0.083472844
3.2	0.36994466	0.086228776
3.3	0.37856754	0.089059588
3.4	0.38747350	0.091962103
3.5	0.39666971	0.094932126
3.6	0.40616292	0.097964304
3.7	0.41595935	0.10105199
3.8	0.42606455	0.10418708
3.9	0.43648326	0.10735988
4.	0.44721925	0.11055895
4.1	0.45827515	0.11377095
4.2	0.46965225	0.11698052
4.3	0.48135030	0.12017016
4.4	0.49336732	0.12332013
4.5	0.50569933	0.12640841
4.6	0.51834017	0.12941069
4.7	0.53128124	0.13230044
4.8	0.54451128	0.13504900
4.9	0.55801618	0.13762583
5.	0.57177876	0.13999878
5.1	0.58577864	0.14213452
5.2	0.59999209	0.14399905
5.3	0.61439200	0.14555836
5.4	0.62894784	0.14677910
5.5	0.64362575	0.14762950
5.6	0.6583887	0.14808019
5.7	0.67319672	0.14810523
5.8	0.68800724	0.14768301
5.9	0.70277554	0.14679722
6.	0.71745526	0.14543766
6.1	0.73199903	0.14360097
6.2	0.74635913	0.14129114
6.3	0.76048824	0.13851980
6.4	0.77434022	0.13530623
6.5	0.78787084	0.13167715
6.6	0.80103856	0.12766615
6.7	0.81380518	0.12331290
6.8	0.82613647	0.11866211
6.9	0.83800268	0.11376237
7.	0.84937892	0.10866476
7.1	0.86024540	0.10342150
7.2	0.87058755	0.098084631
7.3	0.88039601	0.092704710
7.4	0.88966648	0.087329692
7.5	0.89839945	0.082003996
7.6	0.90659985	0.076767758
7.7	0.91427663	0.071656316
7.8	0.92144226	0.066699908
7.9	0.92811225	0.061923558
8.	0.93430461	0.057347155
8.1	0.94003933	0.052985682
8.2	0.94533790	0.048849537
8.3	0.95022285	0.044944957
8.4	0.95471735	0.041274466
8.5	0.95884480	0.037837406
8.6	0.96262854	0.034630402
8.7	0.96609158	0.031647845
8.8	0.96925636	0.028882355
8.9	0.97214460	0.026325167
9.	0.97477712	0.023966539
9.1	0.97717377	0.021796050
9.2	0.97935338	0.019802855
9.3	0.98133367	0.017975970
9.4	0.98313127	0.016304422
9.5	0.98476171	0.014777417
9.6	0.98623945	0.013384450
9.7	0.98757790	0.012115400
9.8	0.98878944	0.010960616
9.9	0.98988550	9.9109285e-3
10.	0.99087659	8.9576962e-3

Shortcuts

• C-c C-c apply formula(only takes 1 step). The table will end up in a weird intermediate state if you do this!
• C-u C-u C-c * iterate until stability. This is the “spreadsheet-like” behaviour that you probably want to use.
• C-c ’ Interactive edit