| Summary: | In this paper, we conduct the comparative analysis of two neural network
approaches to the problem of constructing approximate neural network
solutions of non-linear differential equations. The first approach is
connected with building a neural network with one hidden layer by
minimization of an error functional with regeneration of test points. The
second approach is based on a new continuous analog of the shooting method.
In the first step of the second method, we apply our modification of the
corrected Euler method, and in the second and subsequent steps, we apply our
modification of the Störmer method. We have tested our methods on a boundary
value problem for an ODE which describes the processes in the chemical
reactor. These methods allowed us to obtain simple formulas for the
approximate solution of the problem, but the problem is special because it
is highly non-linear and also has ambiguous solutions and vanishing
solutions if we change the parameter value.
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