The Chebyshev collocation method implemented in Chebfun is used order to solve a class of second one-dimensional singular and genuinely nonlinear boundary value problems. Efforts these problems with conventional ChC have generally failed, the outcomes obtained by finite differences or elements are seldom satisfactory. We try fix this situation using new programming environment. However, for tou...

Using the methods of mathematical analysis and computer algebra, we developed a new reliable algorithm of initial-value method for solving nonlinear singular perturbation problems. To mechanize the algorithm a MatLab procedure called IVPHZ was established. The IVPHZ can handle problems with one or two boundary layers as well as problems with an internal shock layer. Testing of the IVPHZ was mad...

In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...