The book presents in comprehensive detail numerical solutions to
boundary value problems of a number of non-linear differential
equations. Replacing derivatives by finite difference
approximations in these differential equations leads to a system of
non-linear algebraic equations which we have solved using Newton's
iterative method. In each case, we have also obtained Euler
solutions and ascertained that the iterations converge to Euler
solutions. We find that, except for the boundary values, initial
values of the 1st iteration need not be anything close to the final
convergent values of the numerical solution. Programs in
Mathematica 6.0 were written to obtain the numerical solutions.
General
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