# Laguerre collocation solutions vs. analytic results for singular semilinear BVPs on the half line

## Abstract

We make use of two Laguerre collocation techniques as a way to illustrate, deepen or extend some analytic results of existence, uniqueness and asymptotic behavior concerning the solutions to second and third orders nonlinear boundary value problems on the half line. We point out some particular features of solutions, e.g. boundary layers, which have not been noticed by theoretical studies and accurately resolve some analytic singularities. With respect to some challenging BVPs from engineering, we show that not absolutely all the analytic results are validated numerically. The free parameter, i.e., the scaling factor, involved in the Laguerre weight function is adjusted in order to ensure the most efficient convergence of the Newton type algorithms.

## Authors

C.I. Gheorghiu
Tiberiu Popoviciu Institute of Numerical Analysis

## Keywords

Laguerre collocation, scaling, nonlinear equations, unbounded domain, analytic results, singularities, Kidder equation

### References

See the expanding block below.

## Paper coordinates

C.I. Gheorghiu, Laguerre collocation solutions vs. analytic results for singular semilinear BVPs on the half line, ROMAI J., 11 (2015), pp. 69-87

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ROMAI. J

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1841-5512

2065-7714

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