Research ArticleOpen accessPhrase in the titleDiscretized Scheme Examining Convergence and Geometric Ratio Profiles for Control Problem Constrained by Evolution EquationO. OlotuProblem 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 … …Journal of Mathematics and Statistics, Vol. 7, Issue 2 · 18 May 2011 · 7,370 accessesView PDFCite
Research ArticleOpen accessIn the abstractNumerical Solution for 2D European Option Pricing Using Quarter-Sweep Modified Gauss-Seidel MethodKoh Wei Sin, Jumat Sulaiman, Rasid MailProblem statement: This study presents the numerical solution of two-dimensional European option pricing problem based on Quarter-Sweep Modified Gauss-Seidel (QSMGS) iterative method. In fact, the pricing of European option with two-underlying assets can be governed by two-dimensional Black-Scholes Partial Differential Equation (PDE). Approach: The PDE needs to be discretized by using full-, half- and quarter-sweep second-order Crank-Nicolson schemes to generate … …Journal of Mathematics and Statistics, Vol. 8, Issue 1 · 8 Feb 2012 · 7,773 accessesView PDFCite
Research ArticleOpen accessIn the abstractQuadratic Convergence Ratio of Constrained Optimal Control ProblemsO. OlotuProblem statement: Earlier Researchers developed algorithms for solving quadratic control problems, but did not address the quadratic convergence ratio profile. Approach: Hence, the objective of this work is using our developed scheme, Discretized Continuous Algorithm (DCA), to examine both convergence profile and quadratic ratio profile demonstrating the effectiveness and efficiency of the scheme. Methodologically, we obtained generalized unconstrained formulation of … …Journal of Mathematics and Statistics, Vol. 6, Issue 1 · 31 Mar 2010 · 7,372 accessesView PDFCite
Research ArticleOpen accessIn the abstractImbedding the Multiplier in a Discretized Optimal Control Problem With Real Coefficients Via the Penalty and Multiplier MethodsO. OlotuProblem statement: Many earlier schemes, particularly the Function Space Algorithm (FSA) which sidetracks the knowledge of operator, for solving quadratic optimal control problems have been computationally involving and iteratively high. Approach: Though, some of these earlier schemes developed operators consisting of complicated integrals still very difficult to evaluate. Here, objectively, a new scheme, Discretized Continuous Algorithm (DCA), is proposed with … …Journal of Mathematics and Statistics, Vol. 6, Issue 1 · 31 Mar 2010 · 7,041 accessesView PDFCite
Research ArticleOpen accessIn the abstractConvergence Ratio Profile for Optimal Control Problems Governed by Ordinary Differential Equations with Matrix CoefficientsO. Olotu, S.A. OlorunsolaThe geometric convergence ratio, the main focus of a discretized scheme for constrained quadratic control problem was examined. In order to allow for the numerical applications of the developed scheme, discretizing the time interval and using Euler’s scheme for its differential constraint obtained a finite dimensional approximation. Applying the penalty function method, an unconstrained problem was obtained on function minimization … …American Journal of Applied Sciences, Vol. 5, Issue 2 · 28 Feb 2008 · 7,108 accessesView PDFCite
Research ArticleOpen accessIn the abstractOn the Discretized Algorithm for Optimal Problems Constrained by Differential Equation with Real CoefficientsO. OlotuA discretized scheme, Discretized Continuous Algorithm (DCA), for solving constrained quadratic optimal control problems was developed to ease the computational cumbersomeness inherent in some existing algorithms, particularly, the Function Space A lgorithm (FSA) by replacing the integral by a series of summation. In order to accomplish this numerical scheme, we resort to a finite approximation of it by discretizing its … …Journal of Mathematics and Statistics, Vol. 3, Issue 4 · 31 Dec 2007 · 6,851 accessesView PDFCite