@article {10.3844/jmssp.2011.116.123,
article_type = {journal},
title = {Discretized Scheme Examining Convergence and Geometric Ratio Profiles for Control Problem Constrained by Evolution Equation},
author = {Olotu, O.},
volume = {7},
year = {2011},
month = {May},
pages = {116-123},
doi = {10.3844/jmssp.2011.116.123},
url = {https://thescipub.com/abstract/jmssp.2011.116.123},
abstract = {Problem statement: Here, we develop a discretized scheme using only the penalty method
without involving the multiplier parameter to examine the convergence and geometric ratio profiles.
Approach: This approach reduces computational time arising from less data manipulation.
Objectively, we wish to obtain a numerical solution comparing favourably with the analytic solution..
Methodologically, we discretize the given problem, obtain an unconstrained formulation and construct
an operator which sets the stage for the application of the discretized extended conjugate gradient
method. Results: We analyse the efficiency of the developed scheme by considering an example and
examining the generated sequential approximate solutions and the convergence ratio profile computed
quadratically per cycle using the discretized conjugate gradient method.
Conclusion/Recommendations: Both results, as shown in the table, look comparably and this
suggests that the developed scheme may very well approximate an analytic solution of a given
problem to an appreciable level of tolerance without its prior knowledge.},
journal = {Journal of Mathematics and Statistics},
publisher = {Science Publications}
}