Universiti Teknologi Malaysia Institutional Repository

One-step explicit methods for solving stiff differential equations

Ahmad, Rokiah @ Rozita (2006) One-step explicit methods for solving stiff differential equations. PhD thesis, Universiti Teknologi Malaysia, Fakulti Sains.

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Abstract

Stiffness is a special problem which arises in both the ordinary and partial differential equations. It is not only a difficult concept to define but also complicated to solve. For the past fifty years, numerical analysts have studied rigorously the difficulties in solving stiff systems by using implicit methods. This research is focused to develop new one-step explicit methods to combat stiffness. Using the Taylor and Runge-Kutta methods as the basis, we try to develop new one-step explicit methods. We have successfully developed some one-step explicit methods to encounter the stiff problems. This study also deals with the partial differential equation, which shows its stiffness after the process of semidiscretization. For the semidiscretization purposes, the method of lines has been proposed to fulfill the needs. Two kinds of method of lines have been used in the process of discretizing the partial differential equations, namely; the threepoint and the five-point central finite differences. These two kinds of method of lines are composed by means of Runge-Kutta-like methods, which have been developed in this research. The discussions of better accuracy obtained using these new methods to combat stiffness in the ordinary and partial differential equations can be found in Chapters 3, 4, 5 and 6. This study also manages to identify the form of stability for some of the new one-step explicit methods produced and construct the stability regions for all of the methods created. The numerical solution attained proves that the new methods shows excellent accuracy and may become an alternative method for stiff problems. The suggested future research for solving stiff problems using explicit methods are given in the final chapter.

Item Type:Thesis (PhD)
Additional Information:Thesis (Ph.D) - Universiti Teknologi Malaysia, 2006; Supervisor : PM. Dr. Nazeeruddin Yaacob
Uncontrolled Keywords:differential equations, numerical solutions, stiff computation (differential equations)
Subjects:Q Science > Q Science (General)
Divisions:Science
ID Code:18653
Deposited By: Kamariah Mohamed Jong
Deposited On:26 Mar 2014 04:10
Last Modified:26 Mar 2014 04:14

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