Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Supervisors info:
Βασίλειος Δουγαλής Καθηγητής ΕΚΠΑ (Επιβλέπων), Ιωάννης Στρατής Καθηγητής ΕΚΠΑ, Μιχαήλ Δρακόπουλος Λέκτορας ΕΚΠΑ
Original Title:
Μέθοδοι πεπερασμένων διαφορών για προβλήματα δυο σημείων
Summary:
Several problems arising in science and engineering are modeled by differential
equations that involve conditions specified at more than one point. In this
paper we present a method for the solution of two point boundary value problems
for second order ordinary differential equations of the form –(pu’)’+qu=f in
[a,b] where f, p, q are functions with p>0 q0 and u the solution of the
equation with boundary conditions as follows:
If the boundary gives a value to the normal derivative of the problem then it
is a Neumann boundary condition where u’(a)=u’(b)=0. If the boundary gives a
value to the problem then it is a Dirichlet boundary condition where
u(a)=u(b)=0. Finally there may be a combination of the above mentioned where u’
(a)=u(b)=0 ή u(a)=u’(b)=0.
The solution to the problems of that kind is by the use of the finite
differences method on a closed space [a,b]. We put this method to a test by
finding the stability, the numerical rank and the convergence of it in various
problems. Three Matlab implementations of this method are presented afterwards
that confirm the results of this theory.
In conclusion, I would like to recommend this study to students who wish to
have a better approach to the two points finite element method through the
study of numerous applications and examples.
Keywords:
Finite differences, Numerical rank, Stability, Convergence, Equation
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