Discrete invariant imbedding for singular boundary value problems with a regular singularity
A discrete invariant imbedding method is proposed for solving a two-point boundary value problem on the interval [0,b] for a linear second order ordinary differential equation with a singularity of the first kind at \(x=0\). By employing the series expansion on (0,\(\delta\) ], where the free parameter \(\delta\) is the bound for the application of the series expansion near the singularity, the problem is first replaced by a regular one on [\(\delta\),b]. The discrete invariant imbedding method is then applied to solve the problem over the reduced interval. The stability analysis of the method, which can be considered as a kind of three-term recurrence relation, is discussed. Some model problems are solved to compare the numerical results with those of other methods.
scientific article; zbMATH DE number 4016078
scientific article