Abstract:
In this thesis, accelerated tted mesh nite di erence method is presented for solving
Singularly perturbed Self-adjoint boundary value problems. First, the derivatives of the
di erential equation are transformed into nite di erence approximations that make lin ear system of algebraic equations in the form of a three-term recurrence relation which
can easily be solved by Thomas algorithm. And then, Richardson extrapolation method
is applied to accelerate the convergence. Second, establish the convergence of the pro posed method very well. Finally, validate results using numerical model examples and
compared with other methods listed in the literature and exact solution. Maximum
absolute error for each model example shown by tables and behavior of graphs with dif ferent perturbation parameters and mesh sizes which shows the betterment of the present
method.
