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

Journal of Mathematics and Statistics

O. Olotu¹ 

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

DOI  :  10.3844/jmssp.2011.116.123

学科分类：社会科学、人文和艺术（综合）

来源: Science Publications

【 摘 要 】

Problem statement: Here, we develop a discretized scheme using only the penalty methodwithout 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 constructan operator which sets the stage for the application of the discretized extended conjugate gradientmethod. Results: We analyse the efficiency of the developed scheme by considering an example andexamining the generated sequential approximate solutions and the convergence ratio profile computedquadratically per cycle using the discretized conjugate gradient method.Conclusion/Recommendations: Both results, as shown in the table, look comparably and thissuggests that the developed scheme may very well approximate an analytic solution of a givenproblem to an appreciable level of tolerance without its prior knowledge.

【 授权许可】

Unknown