Abstract:
In this thesis, Chebyschev iteration technique has been presented to solve second order
singularly perturbed 1D reaction – diffusion equation for a very small perturbation
parameter, with both variable and constant coefficient of reaction term. The given
problem of interest is discretized and the derivative of the given differential equation is
replaced by finite central difference approximation to obtain system of algebraic
equation. Chebyschev three – level scheme was developed from the two – level scheme to
solve the obtained algebraic equation. To investigate the convergence of the proposed
method, three examples were taken and compared with other methods listed in the
literature and exact solution. The relationship between number of iteration number and
the condition number is analyzed and found to be: the larger the condition number the
slower is the rate of convergence. Finally, pointwise and maximum absolute error for
each example was shown both by table and numerical approximation and exact solution
is demonstrated on the same graph with different iteration number.
