Research Article Open Access

Discretized Scheme Examining Convergence and Geometric Ratio Profiles for Control Problem Constrained by Evolution Equation

O. Olotu

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 of Mathematics and Statistics
Volume 7 No. 2, 2011, 116-123

DOI: https://doi.org/10.3844/jmssp.2011.116.123

Submitted On: 20 July 2010 Published On: 18 May 2011

How to Cite: Olotu, O. (2011). Discretized Scheme Examining Convergence and Geometric Ratio Profiles for Control Problem Constrained by Evolution Equation. Journal of Mathematics and Statistics, 7(2), 116-123. https://doi.org/10.3844/jmssp.2011.116.123

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Keywords

  • Discretized scheme
  • operator v
  • evolution equation
  • examining convergence
  • Conjugate Gradient Method (CGM)
  • control problem constrained
  • numerical solution
  • square integrable
  • penalty parameter
  • conjugate gradient algorithm