Week - 2 - Explicit and Implicit Analysis

Implicit and Explicit analysis

Introduction:

The implicit method is an iterative way of finding the more accurate solution to the problem within the desired tolerance. On the contrary, the explicit method is not iterative or says that it is a direct method of finding the solution to the problems. The implicit method iterates over the answer to check if the answer obtained is converged or not unlike the explicit method. For the same reason implicit method is time-consuming but a very absolute method. The implicit method is trustworthy. The explicit method can or cannot provide one the exact answer. So, one needs to validate the answer obtained by the explicit method.

The way of controlling the explicit method is through the time step interval. It means one needs to decrease the length of small-time intervals for solving large problems. The implicit method is controlled by tweaking the value of tolerances. It is possible that the number of iteration increases with smaller tolerances and becomes computationally demanding.

Discussion and Comparison:

f= u+u3/3
k=1+u2
Implicit	Explicit	External Force
0.00000	0	0
0.81785	1	1
1.28794	1.5	2
1.61099	1.807692308	3
1.85927	2.042007732	4
2.06510	2.235438978	5
2.24231	2.402183809	6
2.39885	2.54988367	7
2.53970	2.683183115	8
2.66820	2.805142193	9
2.78668	2.91789673	10
2.89685	3.023003651	11
3.00000	3.121637074	12
3.09714	3.214706925	13
3.18905	3.302934378	14
3.27638	3.386901837	15
3.35965	3.4670872	16
3.43928	3.543888024	17
3.51566	3.617639001	18

For assignment equation:

f= u3+9u2+4u
k= 3u2+ 18U+4
Implicit	Explicit	External Force
0.00000	0	0
0.17774	0.25	1
0.29616	0.365107914	2
0.39164	0.456250214	3
0.47251	0.534150056	4
0.54420	0.603255453	5
0.60916	0.665950003	6
0.66890	0.723694831	7
0.72444	0.777464893	8
0.77651	0.827950252	9
0.82565	0.875661065	10
0.87227	0.920987365	11
0.91670	0.964235423	12
0.95921	1.005651029	13
1.00000	1.045435049	14
1.03925	1.083754167	15
1.07712	1.120748531	16
1.11372	1.156537327	17
1.14917	1.191222928	18

Learning Outcomes:

• The explicit method is not good as the implicit method unless the number of points is increased
• The explicit method takes very little time to compute the problem then implicit method

Conclusions:

If one is performing the explicit analysis then they must increase the number of points to be calculated for better accuracy and while performing implicit analysis one must tweak the value of convergence for a good result and optimum time.