ABSTRACT
This chapter presents methods to solve problems with one independent variable involving second-order differential equations and first-kind boundary conditions. Additionally, there are situations where second-order differential equations can be reduced to first-order equations. Then, examples of linear and nonlinear second-order differential equations with first-kind boundary conditions are shown. Despite being a second-order differential problem, it could be reduced to two first-order differential equations. Of course, if a zero-order reaction is present, no particular advantage is gained with one form or the other. Nonlinear, second-order differential equation, and an analytical exact solution is very difficult at the least. Several solutions of such problems lead to second-order equations including Bessel differential equations and are therefore excellent examples to be described. In a general situation, the second and other approximations should be obtained and the decision regarding satisfactory solution would emerge from comparisons between the deviations between consecutive approximations.
