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اطروحة Sumaya Abdul Abaas Saify

Abstract

Abstract:
The main aim of this thesis is to study and modify some analytic and numerical methods to treat a system of linear second kind Volterra integral equations. For the analytic treatment two methods for solving single Volterra integral equation including Laplace transform and successive approximation method have been modified to be applicable to solve the system. Runge-Kutta methods including: Runge-Kutta second order, Runge-Kutta third order and Runge-Kutta of fourth order have been modified to give numerical solution to this system and study the convergent of the algorithms of Runge-Kutta methods. In addition, block methods which include: method of two, three and four blocks have been used to find numerical solution to this system. The package “NSSLSKVIE” is constructed to find the numerical solutions to system of linear Volterra integral equations using all the above methods. Finally, at the end of each method, algorithms and programs are developed and written in MATLAB (Version 6.5).



اطروحة Rasheed Basheer Reheima

Abstract

Abstract:
The objective of this thesis is to study and development the solution of linear programming problems with free variables. This thesis studied number of methods with its algorithms to solve the above problems. The thesis studied one of classical methods which expressed any free variable as a difference between two nonnegative variables, then the modified MPS method is studied which expressed any free variables as a function of remaining nonnegative variables . It is found that MPS method is better than classical method, since MPS method reduced the tables number, make the calculations easier and reduced the solution time. Also MPS method used some basic theorems to determine the solution result for some problems from the initial table with out depending on the problem detail solution . This thesis also includes appendix represented the package programs with Visual Basic language (Microsoft Visual Basic 6.0), to get a good forms of display at execution and solving all the problems that may be found in this scope to apply all methods that included in this thesis



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