Theses:
PhD Dissertation
The Galerkin method for singular nonoscillatory two-point boundary value
problems
January 1994, KFUPM, Saudi Arabia
Abstract: The Galerkin method with special patch basis is used for the
approximation of the solution of a general class of second order singular
two-point boundary value problems. Convergence is analysed in several norms.
Higher order convergence in the uniform norm are obtained for special data. The
results are new both for special and general data. The class of problems treated
in this dissertation extends the class of problems treated in the literature in
many directions. The existence, uniqueness and the regularity of the solutions
are not assumed; these are studied in proper places as needed. Both linear and
nonlinear problems are treated in this dissertation.
Download PhD Dissertation
MS Thesis
Stiffly stable 3-step linear multistep methods
March 1986, KFUPM, Saudi Arabia
Abstract: The whole class of 3-step linear multistep methods for
solving system of ordinary differential equations is shown in a parameter space.
All A -stable methods are shown as a subclass. Almost all of the existing
stiffly stable methods of this class are found. The angle for A (a)-stability of
these methods are shown. Particular emphasis is given to develop methods with
least error constant and having large region of instability in the right half
plane which are suitable for stiff systems with the capability of detecting
unstable behavior of a problem. Variable stepsize variable formula methods are
developed from this class. Algorithms are developed for different cases:- fixed
formula with equal stepsize; fixed formula with variable stepsize using Hermite
interpolation; and variable stepsize variable formula method. The algorithms are
embodied in computer codes and these are applied to some examples. The idea can
be extended to higher step linear multistep methods.
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