mod_rll_local_solutions Module

Calculation of the local regular solutions

1. Prepare VJLR, VNL, VHLR, which appear in the integrands TAU(K,IPAN) is used instead of TAU(K,IPAN)**2, which directly gives RLL(r) and SLL(r) multiplied with r. TAU is the radial mesh.
2. Prepare the source terms YR, ZR, YI, ZI because of the conventions used by Gonzalez et al, Journal of Computational Physics 134, 134-149 (1997) a factor $\sqrt(E)$ is included in the source terms this factor is removed by the definition of ZSLC1SUM given below $$\begin{equation} vjlr = \kappa J V = \kappa r j V \end{equation}$$ $$\begin{equation} vhlr = \kappa H V = \kappa r h V \end{equation}$$ i.e. prepare terms $\kappa JDV$, $\kappa HDV$ appearing in 5.11, 5.12.

Then determine the local solutions solve the equations $$\begin{equation} SLV \times YRLL=S \end{equation}$$ and $$\begin{equation} SLV \times ZRLL=C \end{equation}$$ and $$\begin{equation} SRV \times YILL=C \end{equation}$$ and $$\begin{equation} SRV \times ZILL=S \end{equation}$$ i.e., solve system $A U=J$, see eq. 5.68.