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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.